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Emerging market financial crises, investors and monetary policy
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Emerging market financial crises, investors and monetary policy
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EMERGING MARKET FINANCIAL CRISES, INVESTORS AND MONETARY POLICY by Engin Volkan A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree Doctor of Philosophy (ECONOMICS) August 2008 Copyright 2008 Engin Volkan Dedication This dissertation is dedicated to my parents and my close friends, H useyin and Sedef Volkan, to my sister, Damla Pulak, and my wonderful niece, G ok ce Pulak ii Acknowledgements I would like to thank The Department of Economics at The University of Southern California for giving me the opportunity to fulll my ultimate goal. A special thanks to Prof. Jerey Nugent for all his support during my application to the program and to Young Miller, Morgan Ponder and Jennifer Brown, for making my life at the department easy. I am grateful to my advisor, Prof. Vincenzo Quadrini, for his guidance and support which encouraged me in completing this dissertation. My gratitude to my dissertation committee members, Prof. Robert Dekle and Prof. Fernando Zapatero, their suggestions were invaluable. I would like to acknowledge helpful comments from Prof. Michael Magill and Prof. Ayse Imrohoroglu. I extend my thanks to my friends, Rahul Giri, Constance Liu, Rubina Verma. Their presence have made this journey a memorable experience. I would like to thank Nate Arnold and Jacqueline Smith for the suggestions they made throughout the development of the dissertation. My sincere thanks to Inci Ilgin for always being there for me. Lastly, my heartfelt thanks to my parents, my sister and my niece for their belief in me. iii Table of Contents Dedication ii Acknowledgements iii List Of Tables vi List Of Figures vii Abstract ix Chapter 1: Introduction 1 Chapter 2: Sovereign Default Risk, Risk Averse Investors and Financial Contagion 6 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Empirical Assessment of Emerging Markets in the 1990s . . . . . . . . . . 10 2.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Characterization of Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 The Timing of Decisions . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.2 The Recursive Problem . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4.2.1 Sovereign's Problem . . . . . . . . . . . . . . . . . . . . . 20 2.4.2.2 Investor's Problem . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Analysis of Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5.1 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5.2 Properties of Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 27 2.5.2.1 Equilibrium Value Functions . . . . . . . . . . . . . . . . 27 2.5.2.2 Equilibrium Default Policy . . . . . . . . . . . . . . . . . 27 2.5.2.3 Equilibrium Debt Policy . . . . . . . . . . . . . . . . . . 30 2.5.2.4 Equilibrium Bond Prices . . . . . . . . . . . . . . . . . . 30 2.5.3 Contagion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.5.3.1 Properties of Equilibrium . . . . . . . . . . . . . . . . . . 33 2.5.4 Quantitative Analysis of Equilibrium . . . . . . . . . . . . . . . . . 36 2.5.4.1 Simulation Results of The Model . . . . . . . . . . . . . . 36 2.5.4.2 Contagion: Impulse-Response Simulations . . . . . . . . . 38 2.5.4.3 Contagion versus Default Eects on Bond Prices . . . . . 40 iv 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Chapter 3: In ation Targeting in Emerging Economies: Interest Rate Rules Matter 44 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2.2 Foreign Demand for Domestic Goods . . . . . . . . . . . . . . . . . 51 3.2.3 Wholesale Producers . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.2.4 Capital Producers . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.2.5 Retail Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2.6 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2.7 Resource Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.8 Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.8.1 Simple Interest Rate Rules . . . . . . . . . . . . . . . . . 62 3.2.8.2 Smoothing Interest Rate Rules . . . . . . . . . . . . . . . 63 3.2.8.3 Forward-Looking Simple Interest Rate Rule . . . . . . . . 63 3.2.8.4 Forward-Looking Smoothing Interest Rate Rule . . . . . 64 3.3 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4 Quantitative Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.4.0.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . 68 3.4.0.6 Impulse Responses . . . . . . . . . . . . . . . . . . . . . . 71 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Reference List 74 Appendix A Numerical Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 A.1 Proofs of The Equilibrium Features of The Three-Country GEIM Model . 92 A.2 Solving The Three-Country GEIM Model . . . . . . . . . . . . . . . . . . 92 A.3 Solving The SOE Financial Accelerator Model . . . . . . . . . . . . . . . 95 A.3.1 System of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 95 A.3.2 Non-Stochastic Steady-State . . . . . . . . . . . . . . . . . . . . . 97 A.3.3 Log-Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Appendix B Data Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 B.1 Summary of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 v List Of Tables 2.1 Spread Correlations, Countries (Adjusted to International Shocks) . . . . 14 2.2 Trade Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Spread Correlations, Regions . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5 Real GDP (USD bln), 1995 prices . . . . . . . . . . . . . . . . . . . . . . 26 2.6 Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.7 Total External Debt (% of GDP) . . . . . . . . . . . . . . . . . . . . . . . 43 3.1 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2 Simple Interest Rate Rules . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3 Loss of Interest Rate Rules: CPI . . . . . . . . . . . . . . . . . . . . . . . 70 vi List Of Figures 2.1 EMBI Spreads versus Net Portfolio Flows to EMs, 1990-2001 . . . . . . . 11 2.2 Net Capital Private Flows versus Net Portfolio Private Flows, Billion US Dollars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Value Functions and Equilibrium Default Policy . . . . . . . . . . . . . . 31 2.4 Equilibrium Debt Policy and Bond Prices . . . . . . . . . . . . . . . . . . 32 2.5 The Representative Investor's Wealth . . . . . . . . . . . . . . . . . . . . 34 2.6 Wealth versus Value of Default and No-default . . . . . . . . . . . . . . . 35 2.7 Contagion: Impulse-Response Simulation . . . . . . . . . . . . . . . . . . 39 3.1 Loss of Simple Interest Rate Rule, CPI . . . . . . . . . . . . . . . . . . . . 69 3.2 All Interest Rate Rules, CPI I . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.3 All Interest Rate Rules, CPI II . . . . . . . . . . . . . . . . . . . . . . . . 76 3.4 All Interest Rate Rules, CPI III . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5 All Interest Rate Rules, CPI IV . . . . . . . . . . . . . . . . . . . . . . . . 78 3.6 Simple versus Forward-Looking Smoothing Interest Rate Rule, CPI I . . . 79 3.7 Simple versus Forward-Looking Smoothing Interest Rate Rule, CPI II . . 80 3.8 Simple versus Forward-Looking Smoothing Interest Rate Rule, CPI III . . 81 3.9 Simple versus Forward-Looking Smoothing Interest Rate Rule, CPI IV . . 82 vii 3.10 External Balance Adjustments: Simple Rule versus Forward-Looking Smooth- ing Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.11 Forward-Looking Smoothing Interest Rate Rule: Dierent Smoothing Fac- tors, CPI I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.12 Forward-Looking Smoothing Interest Rate Rule: Dierent Smoothing Fac- tors, CPI II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.13 Forward-Looking Smoothing Interest Rate Rule: Dierent Smoothing Fac- tors, CPI III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.14 Forward-Looking Smoothing Interest Rate Rule: Dierent Smoothing Fac- tors, CPI IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 viii Abstract This dissertation consists of two essays. The rst essay brings a competing expla- nation for the channel of contagious emerging market crises of the 1990s. It develops a three-country GEIM model to show a debt crisis in one emerging market country trans- mits to others via common investors through the world interest rate. This constitutes an alternative explanation to the literature suggesting that contagion is due to liquidity, incentives problems or imperfect information or ight to quality. Quantitative analysis of the equilibrium show that the model can explain 60% of the correlation across the emerg- ing market bond spreads since the 1990s. The high correlation across the spreads has often been documented by papers as an important indicator of nancial contagion even at times of no-crisis. Additionally, the model can explain 50% of the average debt-to-GDP ratio observed across emerging market economies during the 1990s. One of the goals of any model in sovereign default literature is to generate an equilibrium that sustains a large debt-to-income ratio. The second essay contributes to the literature in proposing alternative interest rate rules for in ation targeting. It introduces a SOE model built on the nancial accelerator framework. The model is solved quantitatively and simulated. First set of results suggest that in targeting in ation the dynamics of consumer rather than domestic price index should be the focus. This is mainly because when consumer ix price index is the target the exchange rate becomes a determinant in policy response and enables the authority to reduce the distortion on the return to capital that may arise due to liability dollarization. Second set of results suggest that forward-looking smoothing interest rate as a policy rule achieves the least volatility in the economy. Final set of re- sults suggest that the monetary authority should adopt a regime switching policy during nancial distress, where at the start of the distress the domestic interest rate should be adjusted according to the forward-looking smoothing rule and, once the economy returns to its pre-shock output level, the authority should switch to a simple rule. x Chapter 1 Introduction During the 1990s the emerging market economies have undergone a number of crises- most striking examples of which are the 1994-95 Mexican Tequila Crisis, 1996- 1997 East Asian Crises, 1998 Russian Default. These crises were characterized by a set of empirical regularities that were identied as simultaneous sudden reversal of capital in ows to a group emerging economies, followed by sharp recessions, sharp corrections in asset prices and large depreciations. With the onset of these crises, the urge to gain a better understanding of the contagious emerging market crises has led to a rapid growth in literature. In studying this phenomenon, the challenge is to be able to explain why emerging nancial markets are prone to crises and what are the channels of contagion. The rst essay of this dissertation contributes to the literature in the latter aspect. It provides an explanation to how contagion may arise across emerging debt markets. In the essay, a three-country general equilibrium incomplete markets model is developed to show that a debt crisis in one emerging market country transmits to the others via common investors through its eect on the world interest rate. This constitutes an alternative explanation to the existing literature, such as those suggest that contagion arises due to 1 ight to quality [41], liquidity or incentive problems [11] and incomplete information or information asymmetry [37]. The model environment consists of two emerging market economies and a developed economy which is populated by a continuum of investors. The emerging economies are open economies that are small relative to the developed economy but not small open economies. Thus, their debt-default policy has a non-negligible impact on the nancial markets. Additionally, they are fundamentally unrelated to each other and do not have any trade or direct nancial links. However, they are linked to each other through the aforementioned investors that lend to both of these emerging economies. The investors are identical, risk averse and follow an investment strategy that requires them to avoid declines in the value of their portfolio below zero. The medium of lending is long- lived coupon bonds. The bonds are issued by the sovereign of the emerging economies. Each bond is a contract where the sovereign agrees to make coupon payments. However, if the economy is highly indebted and receives a negative income shock, it may opt to default on its payments. Default is determined according to an incentive constraint, similar to the one introduced in the seminal work by [20]. If the economy defaults, it incurs a proportional income loss and stay in partial nancial autarky for only one period during which it is not allowed to borrow but are allowed to leave a portion of its outstanding debt in the market. Default in this model is the trigger to contagion such that a debt crisis in one of the emerging economies would imply a drop in the investor's value of portfolio which would induce the investors to reduce their supply of funds to the international debt markets. In equilibrium, decline in the supply of funds would generate an increase the world interest rate which is in fact an increase in the borrowing costs for other emerging economies or a drop in their bond prices. The model 2 developed in this essay contributes to the literature as it can also explain two important empirical facts of the 1990s often highlighted by the literature: high debt-to-income ratio observed across the emerging market economies(50% on average) and high correlation across the emerging market bond spreads(0.83 on average). According to the simulation results, the model can explain 60% of the correlation across the emerging market bond spreads. The high correlation across the spreads has often been documented by empirical papers as an important indicator of nancial contagion even at times of no-crisis. In addition to this, the model can explain more than 50% of the average debt-to-income ratio observed across emerging market economies. One of the goals of any quantitative model in sovereign default literature is to be able to generate an equilibrium that sustains a large debt to income ratio. During the 1990s, xed exchange rate regime was proved as an unsustainable monetary policy. After the 1990s, emerging economies started to adopt exible exchange rate regimes with a strong commitment to in ation, by means of interest rate as a policy instrument. As of 2006, emerging economies which adopt the aforementioned monetary policy rule are Brazil, Chile, Mexico, Philippines, South Africa and Turkey. Although there is a growing literature which suggest in ation targeting for emerging economies, the extend to what type of interest rate rule should be adopted is still being questioned. The second essay of this dissertation contributes to the literature in proposing alternative interest rate rules for in ation targeting. It examines the performance of four alternative interest rate rule for in ation targeting in an emerging economy. The model used in the essay is a modied version of [28] that is a small open economy model built on the so-called nancial accelerator framework with price rigidities a la [9]. The nancial accelerator 3 framework is well-known for its competency in explaining the balance sheet problems that arise during emerging market crises, mainly in the form of currency mismatches and non-performing loans. The model consists of three types of producers: wholesale, capital and retail, and three types of agents: households who own the retail rms, entrepreneurs who manage the wholesale rms, and capital producers. The capital producers utilize domestic and foreign nal goods in the production of the capital good; the wholesale producers employ the capital good as an input; the retail rms utilize wholesale goods to produce dierentiated goods that are aggregated into the nal good; the households receive labor income, prots and asset returns from which they can consume a composite good of domestic and foreign nal goods. In the model, there is also a government which follows a balanced budget policy and nally, a monetary authority which determines the domestic interest rate via a policy rule. The policy rules are of four types: a simple Taylor rule, a forward-looking Taylor rule, a smoothing interest rate rule and a forward- looking smoothing interest rate rule. The model is calibrated to match certain features of the Korean economy of the 1990s. The rst set of quantitative results which consists of the simulated loss of the alternative interest rate rules suggest that in targeting in ation the monetary authority should focus on the dynamics of consumer price index rather than domestic price index. This is mainly because the when consumer price index is the in ation target the exchange rate becomes a determinant in policy response and this enables the monetary authority to reduce the distortion on the return to capital that may arise due to high liability dollarization in the economy. Note that under in ation targeting with a special focus domestic price index the monetary authority completely ignores the changes in exchange rate. This in return amplies the distortionary on return 4 on capital due to nancial market imperfections and high liability dollarization within the real sector. The second set of quantitative results suggest that a monetary authority of an emerging economy should adopt forward-looking smoothing interest rate as a policy rule which achieves the least volatility in the economy. Finally, the last set of results suggest that the monetary authority should adopt a regime switching policy in case of a nancial distress, where at the start of the distress the authority adjust the domestic interest rate according to the forward-looking smoothing interest rate rule and, once the economy returns to its pre-shock output level, the authority switches to using the simple interest rate rule. 5 Chapter 2 Sovereign Default Risk, Risk Averse Investors and Financial Contagion 2.1 Introduction Emerging market nancial crises in the 1990s were contagious in nature. Con- tagion was identied as the spread of adverse nancial shocks across countries in the form of simultaneous depreciation in exchange rates and drops in equity and bond prices following rapid reversals of capital in ows. Studies suggest the existence of investors com- mon to all economies as the primary channel of contagion 1 , rather than factors like trade 1 [36] compare a group of countries clustered along the lines of trade links versus countries with common bank creditors, and conclude that common nancial linkages better explain the observed pattern of contagion. [24] and [34] show evidence to support the idea that U.S. mutual funds have engaged in contagion trading, i.e. systematically selling stocks from one country when stock prices are falling in another, that played an important role in spreading shocks throughout Latin America. Using portfolio ows into and out of countries during 1994-1998, [25] nd evidence that suggest institutional investors could be a channel for spread of shocks across regions. Other empirical studies that suggest common creditors as a factor behind contagion are [13], [6], [40] and [47]. 6 links or common shocks 2 . The conventional view is that common investors cause conta- gion when they fall into liquidity, incentives or coordination problems or have imperfect information 3 . This paper shows that contagion across emerging economies' sovereign bond markets could also be explained via common investors through world interest rate. The model is a three-country general equilibrium incomplete markets model featuring endogenous default. It consists of two emerging economies and a developed economy populated by a continuum of investors. The emerging economies are fundamentally independent from each other with no direct nancial or trade links. However, they are nancially linked to each other via the investors who lend to both emerging economies. The medium of lending is state non-contingent and long-lived coupon bonds. Each bond represents a contract between an emerging economy's sovereign and the investor in which both sides agree to fulll the terms of the contract. However, a contract has limited enforceability on the emerging economy's side as the sovereign may opt to default on any of their coupon payments until the bond matures. This introduces a contingency into contracts and fa- cilitates interstate smoothing. In this paper, default is used as a trigger to contagion. Accordingly, a default (or an increase in default risk) of an emerging economy's sovereign translates into loss for the investor in the form of a decline in the value of their portfo- lio, i.e. wealth. When investors suer a loss they become absolutely more risk averse. Thus, the investors decide to demand fewer risky bonds. In equilibrium, this translates 2 [29] and [21] empirically show that trade links was the main factor behind contagious currency crises that happened between 1959-1993. Trade links for contagion is used in the theoretical works by [27], [17]. On the other hand, [12] show that there is signicant co-movement between capital ows to Latin America and the US interest rates. 3 Some examples that use various investor behavior as the source of contagion are [3], [10], [11], [37]. 7 into a simultaneous decline in emerging market bond demand and prices. The wealth eect is generated by assuming that the investors having decreasing absolute risk averse preferences, more specically logarithmic utility, commonly used in the asset-pricing lit- erature. By using logarithmic utility, the model can generate the so-called contagion trading behavior of mutual funds identied in [35]. The paper departs from the existing literature in three respects. First, it treats the emerging economies as open economies that are non-price takers. This enables the model to closely track the interplay between the debt-default policies of the emerging economies' sovereign and the world interest rate. [31] shows that the correlation of bond returns between mature and emerging markets is 0.53. Second, by using long-lived coupon bonds it introduces annuity into the sovereign default literature. This expands the informational content of the bond prices such that they not only contain the investors' expectations of an imminent default but also the expectations of future default at any point in time to maturity. Finally, it allows the defaulters to continue to have access to nancial markets immediately after default conditional on some outstanding debt recovery. Quantitative analysis of the equilibrium shows that the aforementioned characteristics of the model can contribute to the explanation of important features in the data. According to the simulation results, the Sharpe ratio of the emerging bond market is 0.20 which is 34% of the Sharpe ratio during the 1990s 4 . The model can generate correlation between bond spreads across countries as high as 0.49 which is 60% of the average correlation observed during the 1990s. Consistent with the data, in the model emerging economies have a high mean debt-to-income ratio of 36:6% which is a distinguishing feature of emerging 4 This ratio is calculated from the data reported in [31]. 8 economies. Finally, according to model simulations, the mean default probability is 10%. This value is close to the one calculated by [44] from the data (13:3%). The paper is related to the contagion literature which studies the wealth eect channel, [39], [30] and [41]. In all the three papers, investors with decreasing absolute risk averse preferences spread nancial contagion across emerging economies as they respond to nan- cial losses by reducing their risky investments. However, all these papers study contagion in a dierent framework. [39] study contagion in a partial equilibrium continuous-time model with two risky assets and three type of traders: noise traders who trade randomly in one of the markets, long-term investors who trade assets based on their fundamentals and convergence traders who follow a short-term investment strategy in both markets. According to their framework, contagion across markets occur either when fundamentals in one of the markets deteriorate or noise traders generate volatility in the market returns lead to a trading loss for the convergence traders. [30] study contagion in a variant of a self-fullling crises model. They assume common investors as investment banks. Accord- ing to their model, an investment bank who suers a wealth loss in an emerging economy during crisis causes contagion as it becomes more risk averse and reduces its investments in another emerging economy. As a result of this a crisis becomes more likely to occur in the other country. Finally, [41] studies contagion in a general equilibrium small open economy model which is a variant of the model introduced in [20]. The model consists of two emerging economies and a mutual fund which is common to the two economies. In the international nancial markets, the mutual fund trades two risky one-period discount bonds and a risk-free bond with an exogenously xed interest rate. According to her model, contagion occurs when a mutual fund incurs a wealth loss due to default and 9 shifts its demand from risky bonds to risk-free bond. Thus, contagion occurs in the form of ight to quality. The rest of the paper consists of ve sections. In section 2.2, the data on private capital ows to emerging economies and the dynamics in the emerging bond markets during the 1990s are analyzed. The model is introduced in section 3.2. Section 2.4 presents the characterization and the denition of equilibrium. In section 2.5, the model is qualitatively and quantitatively analyzed. Finally, section 3.5 concludes. 2.2 Empirical Assessment of Emerging Markets in the 1990s This section presents some empirical regularities observed in emerging bond markets during the 1990s. The data used are JP Morgan's Emerging Market Bond Indices (EMBI and EMBI+) and Institutional Investor Ratings (IIR). The details on the content and the frequency of the data are provided in Appendix B.1. During the period of 1994-2001, emerging bond markets displayed the following empirical regularities: 1. Emerging market bond spreads were high and volatile. 2. Emerging market bond spreads followed a systematic pattern closely related to capital ows. 3. There was a signicant comovement of emerging market bond spreads within and across regions. Emerging market bond spreads, as a price of risk, were high and volatile ranging between 200-2000 basis point (Figure 2.1). Bond spread is dened as the dierence be- tween the return of risky bond and a safe bond, i.e. U.S. T-bill rate. According to 10 Oct91 Mar93 Jul94 Dec95 Apr97 Sep98 Jan00 May01 Oct02 200 400 600 800 1000 1200 1400 1600 1800 2000 1990 1992 1994 1996 1998 2000 2002 −40 −20 0 20 40 60 80 100 120 (a) EM Bond Spreads (basis point) (b) Net Portfolio Flows to EM (USD bln) Figure 2.1: EMBI Spreads versus Net Portfolio Flows to EMs, 1990-2001 EMBI/EMBI+ spreads and IIR, during the 1990s, investors incorporated their percep- tion of risk into bond prices by asking for higher risk premium. This phenomenon was particularly evident in times of nancial crisis. The bond spreads were also highly volatile due to the fact that the investor base was outnumbered by crossover investors, relative to dedicated investors. Crossover investors are non-bank investors which include global and high-yield funds, pension funds, insurance companies, and a proprietary trading desks of investment banks. These investors provide smaller investors with a means of diversifying risk and providing risk-return opportunities. Crossover investors have superior capacity to absorb and process information and conduct a large volume of transactions at a lower cost of intermediation. In contrast to the dedicated investors, which adopt long-term value based investments, crossover investors are known to follow short-term investment strategies that seek opportunistic trade, which increase the volatility of the markets. Volatility increases even more at times when risks in the emerging markets increase or when investors' risk aversion increases. Crossover investors tend to scale back or even 11 eliminate all of their emerging market assets during such episodes [46]. During the 1990s, as a measure of excess return per unit of risk, Sharpe ratio of the emerging bond market was 0.59 5 . Throughout the period of 1994-2001, the emerging market bond spreads followed a systematic pattern closely related to capital ows to emerging economies. In the 1990s, portfolio investments became an important source of external nancing in emerging mar- kets (Figure 2.2). It has increased substantially from the 1980s to the 1990s, accounting for almost 40 percent of the private capital ows into emerging economies. The increase in portfolio ows was steady from the beginning of 1990 until 1994. In the aftermath of the Mexican Peso crisis, the portfolio ows to emerging economies dropped by 64 percent. The most dramatic drop in the in ows was in the Latin American markets whereas some of the East Asian countries were unaected. Portfolio in ows recovered in all adversely aected emerging economies soon thereafter. The recovery lasted until the 1997 Thai Baht crisis which immediately aected not only the Asian markets, but also all other emerging markets. There was a severe out ow from all emerging markets. This ight was even more accentuated in 1998 with the Russian default. The pattern of spreads closely followed the aforementioned dynamics of capital ows. Accordingly, the spreads surged at times of crises and declined after capital returned to the emerging economies (Figure 2.1). The correlation between emerging market bond spreads were considerably high within and across regions. For the period of 1994-2001, the correlations between 11 emerging 5 Annual return and its standard deviation are taken from [31] 12 1980 1985 1990 1995 2000 0 50 100 150 200 250 300 350 Emerging Economies 1980 1985 1990 1995 2000 −20 0 20 40 60 80 100 120 Western Hemisphere 1980 1985 1990 1995 2000 −50 0 50 100 Asia, crisis countries 1980 1985 1990 1995 2000 −40 −20 0 20 40 60 80 Middle East, including Turkey Net private capital flows Net private portfolio flows Figure 2.2: Net Capital Private Flows versus Net Portfolio Private Flows, Billion US Dollars economies vary between 35-99 percent (Table 2.1), out of which only four of them remain below 50 percent. After the eects of common shocks 6 and the trade elasticities (Table 2.2) are taken into account, the results suggest that nancial links play a signicant role in explaining the high correlation across markets, while common shocks and trade links appear to be less important. 6 The risk-free rate, i.e. 3-month US Treasury Bill rate, is used as an indicator of common shocks. 13 Table 2.1: Spread Correlations, Countries (Adjusted to International Shocks) ARG BRA ECU MEX MOR NIG PAN PER POL RUS VEN ARG 1 BRA 0.88 1 ECU 0.60 0.69 1 MEX 0.88 0.98 0.62 1 MOR 0.90 0.98 0.62 0.99 1 NIG 0.89 0.95 0.79 0.93 0.94 1 PAN 0.92 0.96 0.72 0.95 0.97 0.98 1 PER 0.89 0.97 0.69 0.96 0.98 0.97 0.99 1 POL 0.88 0.95 0.69 0.95 0.95 0.97 0.97 0.97 1 RUS 0.37 0.59 0.80 0.48 0.48 0.57 0.52 0.52 0.46 1 VEN 0.89 0.99 0.72 0.97 0.98 0.96 0.97 0.97 0.95 0.61 1 Source: JP Morgan EMBI+, 1994-2001 All values are signicant with zero p-values Table 2.2: Trade Elasticities Countries Trade Elasticity Standard Deviation t-statistics Argentina -0.69 0.384 -1.822 Brazil 0.13 0.015 8.743 Bulgaria 0.64 0.058 11.154 Ecuador 0.02 0.004 4.446 Mexico 0.42 0.021 19.736 Morocco 0.58 0.137 4.250 Nigeria 0.09 0.042 2.214 Panama -2.30 0.691 -3.323 Peru 0.002 0.086 0.027 Poland 0.51 0.021 24.238 Russia -0.04 0.013 -3.003 Venezuela 0.11 0.018 6.367 Source: International Financial Statistics, IMF, 1994-2001 monthly data For the period between 1998-2001, the correlation of emerging market spreads across regions such as Europe-Latin America, Latin America-Africa and Africa-Asia, are high and signicantly positive (Table 2.3). 14 Table 2.3: Spread Correlations, Regions Africa Asia Europe Latin Africa 1 Asia 0.52 1 Europe 0.27 -0.19 1 Latin 0.76 0.35 0.46 1 Source: JP Morgan EMBI+ Spreads, 1998-2001 All values are signicant with zero p-values 2.3 The Model The model is set up in a general equilibrium incomplete markets framework. It fea- tures endogenous default and contagion. The model consists of J emerging economies and a continuum of homogeneous investors. Emerging Economies: There are J emerging economies that are fundamentally unrelated to each other. The economies are indexed by j 2 J. The objective of the emerging economy's sovereign is to maximize the lifetime utility, U : R T + ! R, of the representative consumer whose consumption stream is given as c j = fc j t g 1 t=0 . The lifetime utility function is assumed to be time separable, i.e. there exist identical period constant relative risk averse (CRRA) utility functions u that are continuous, strictly concave and strictly monotonic over period consumption allocation c j t such that U(c j ) =E 0 1 X t=0 t u(c j t ) (2.1) where 0<< 1 is the time discount factor of the representative household. 15 Each period, the emerging economyj is endowed with incomey j t . The level of income is uncertain as it is subject to idiosyncratic transitory shocks 7 , given as j t . These shocks are assumed to follow a rst-order stationary autoregressive process j t = j j t1 + j t (2.2) with coecient j 2 (0; 1) and random variable j t . Each random variable j t is iid across time and economies. They are assumed to have normal distribution with zero mean and j standard deviation, j t N(0; 2 j ). Thus, income is log-normally distributed and is characterized as y j t = exp( j t )y j (2.3) with mean y j . The emerging economies' income process is known by the investors. Each emerging economy insures itself against the aforementioned income uncertainty by borrowing from the investors in the emerging economies' sovereign bond market by issuing coupon bonds. Each coupon bond is traded between the issuer and the investors. Thus, there is no direct nancial link between the economies. In addition to this, the trade links between economies are ignored. Representative Investor: There is a continuum of investors in the international nancial markets. The investors are common to all emerging economies and represent 7 [2] show that emerging economies, unlike developed economies, are characterized by regime switches, a premise motivated by the dramatic reversals in scal, monetary and trade policies observed in these economies. Thus, shocks to trend growth are the primary source of uctuations in these markets as opposed to transitory uctuations around the trend. In this paper, income is only subject to transitory shocks. Shocks to trend growth would not change the results qualitatively. 16 mutual funds. Mutual funds constitute a large part of the institutional investors and are the main channel of nancial ows to emerging economies. Since the investors are assumed to be identical, therefore from this point on the focus will be the representative investor. The representative investor has a lifetime utility functionU i :R T + !R associated with the consumption stream x = (fx t g 1 t=0 ). The lifetime utility function is time separable, continuous, strictly concave, and strictly monotonic over period consumption allocation x t such that U i (x) =E 0 1 X t=0 t u i (x t ) (2.4) where 0 < < 1 is the time discount factor of the representative investor. The repre- sentative investor is assumed to have decreasing absolute risk averse (DARA) preference. With this type of preferences, the representative investor follows a short-term investment strategy that avoids declines in its wealth. Hence, whenever its wealth receives an adverse shock, the investor would recompose its overall portfolio reducing the weight of its risky bond holdings. In equilibrium, this would reduce the price of risky bonds in the interna- tional nancial market. In this respect, DARA preferences are a good approximation for the investor's contagion trading observed in the 1990s [[34] and [35]]. The representative investor trades in two separate markets, namely the mature and the emerging markets. Thus, the investor's wealth is composed of a deterministic part m which is the value of its investments in the mature market and the stochastic part ! t which is the value of its investments in the emerging market. The uncertainty in the 17 value of the investor's investments in the emerging market arises from the default risk. The value of the investor's investments in the mature markets are deterministic because assessing the eect of common shocks on emerging economies that originates from mature markets is not the main focus of this paper. Bonds and Limited Contract Enforceability: There are J emerging economy bonds traded in the emerging markets. The bonds are state non-contingent and long- lived 8 coupon bonds, denoted byb j t for allt. The coupon rate is exogenously given. Each bond j represents a contract signed between the sovereign of the emerging economy j and the representative investor. The contract species the amount traded, the coupon payment promised to be delivered, and the price of the bond. However, the contract has limited enforceability on the emerging economy's side, thus the sovereign may opt to default on its debt obligations, i.e. coupon payments. The sovereign opts to default when the value of default is at least as high as the value of no-default, however at a cost. In case of default, the economy faces two types of direct default penalties: a proportional income loss and one-period partial nancial autarky. The proportional income loss, denoted by 2 [0; 1], is a reduction in income that is attributed to the decline in investments following the default. Additionally, in case of default, the economy enters into a one- period partial nancial autarky during which the sovereign is required only to recover part of their outstanding debt level in the market. The recovery rate is determined by the sovereign. Temporary nancial autarky with debt renegotiation or recovery has been 8 During the 1990s, on average 80% of the outstanding debt of emerging market economies, such as Argentina, Brazil, Russia and Turkey, was long-term debt. Moreover, their debt maturity was on average 16 years. 18 center of attention for an extensive literature on sovereign default [[22], [16], [26], [48] and [32]]. Bond Prices: In this model, the equilibrium emerging economy bond prices are the expected discounted future payos of the bonds. The equilibrium emerging economy bond prices contain both default and contagion risks. The contagion risk arises when an emerging economy's coupon payment and debt rollover become too costly due to factors beyond the economy's own fundamentals. On the other hand, the default risk arises when an emerging economy's own fundamentals deteriorate. Moreover, since the emerging economy bonds have a long-term structure, the bond prices contain not only the imminent, but also the future default and contagion risks. This feature of the bond prices expands the informational content of the bond prices. 2.4 Characterization of Equilibrium This section characterizes the equilibrium of the model. The timing of decisions is explained and the recursive problem is characterized, and the equilibrium is dened. 2.4.1 The Timing of Decisions At the beginning of period t, the transitory income shock j t is realized. Given the state, the emerging economyj's sovereign decides to default or not on its coupon payment. If the sovereign defaults then the economy incurs an income loss and remains in one-period nancial autarky. During partial nancial autarky, the sovereign can only rollover part of its outstanding debt level. If the sovereign does not default then it revises its debt policy for the next period. In the aftermath of default/no-default announcements of all 19 the economies, the emerging economy bond market opens. In the market, the sovereigns and the representative investor, who also revises his or her portfolio allocation, trade the bonds. The period ends when the economies and the investor buy consumption goods. 2.4.2 The Recursive Problem Let the state of the economy j at timet bes t = (y t ; b t ) where y t = (y 1 t ;:::;y j t ;:::;y J t ) and b t = (b 1 t ;:::;b j t ;:::;b J t ) are the vector of the emerging economies' time t income and outstanding debt level, respectively. For all t and for anyj,s t belongs to the state space S = Q 8 j2 J Y j Q 8 j2 J B j . For all j, Y j R + and B j R. 2.4.2.1 Sovereign's Problem For any states t 2S and any periodt, the sovereign of the emerging economyj would default if and only if the following holds V d t (s t ) V n t (s t ) (2.5) where V d t (s t ) and V n t (s t ) are the value of default and no-default, respectively. Then, let d j t (s t ) be an indicator function for default/no-default such that d j t (s t ) = 8 > > > > < > > > > : 1 V d t (s t ) V n t (s t ) 0 otherwise (2.6) 20 Equation (2.5) is a variant of individual rationality condition of debt that has been used by the sovereign default literature. It endogenizes the debt limit by letting the sovereign to default at a point where debt obligations become too costly. The coupon rate and outstanding debt is denoted by e2 (0; 1) andjb j t j, respectively. Bond price is denoted by q j t . Let the optimal value of the economy be V o t : S!R such that for any t and state s t 2S, V o t (s t ) = maxfV d t (s t );V n t (s t )g (2.7) where the value of default for the economy j, V d t :S!R is given by V d t (s t ) = max 0b j t+1 <b j t n u((1)y j t q j t (s t )(b j t b j t+1 )) + EV o t+1 (s t+1 ) o 8t (2.8) and the value of no-default for economy j, V n t :S!R is given by V n t (s t ) = max 0b j t+1 B n u(y j t q j t (s t )(b j t b j t+1 )eb j t ) + EV o t+1 (s t+1 ) o 8t (2.9) Notice that in the value of no-default the indebtedness cannot exceed an ad-hoc natural debt limit B < 0 which prevents a Ponzi scheme. However, this condition will never be binding as the sovereign would only borrow to the extent that it could rollover its debt. Otherwise, it would default, which restrains it from borrowing. 21 2.4.2.2 Investor's Problem The investor's problem is a standard portfolio problem with nitely many assets. The investor maximizes utility (2.4) subject to budget constraint. The maximization problem is given by max xt;z j t+1 E 0 1 X t=0 t ln (x t ) subject to x t + J X j=1 q j t (s t )z j t+1 =m +! t 8t (2.10) x t 0 8t; ! 0 0 z j t 0 8j;8t where ! t follows the process given as ! t = J X j=1 (q j t (s t ) +e(1d j t ))z j t 8t (2.11) Equation (2.11) clearly shows that the investor's wealth process is aected directly by default decisions of the sovereigns. Moreover, equation (2.10) shows how an adverse shock to wealth could constrain the investor's consumption which would aect the bond prices. The following rst order conditions will show the direct relationship between bond prices and investor's wealth level. 22 The rst order conditions of the above maximization problem are x t : t u 0 (x t ) = t (2.12) z j t+1 : t q j t (s t ) =E t h t+1 (q j t+1 (s t+1 ) +e(1d j t+1 )) i 8j (2.13) t :m +! t J X j=1 q j t (s t )z j t+1 x t 0 if t = 0 or = 0 if t > 0 (2.14) The above rst order conditions could be rearranged to characterize market prices of bonds for any j such that q j t (s t ) = E t h M t+1 (q j t+1 (s t+1 ) +e (1d j t+1 )) i 8t (2.15) The variable M t+1 = (u 0 (x t+1 )=u 0 (x t )) is the representative investor's discounted marginal rate of substitution, i.e. the stochastic discount factor. Note that the payo has a direct positive eect on investor's consumption due to an increase in wealth and utility is a concave function. Thus, the covariance between the stochastic discount factor and emerging economy's future payos is non-positive. Moreover, iterating equation (2.15) forward the equilibrium bond price can be written as q j t (s t ) = E t P 1 k=1 h M t+k e (1d j t+k ) i (2.16) showing that the investor incorporates not only the imminent, but also the future default risks, as was mentioned above. 23 Denition 2.4.1 (Recursive Equilibrium) A recursive equilibrium is a set of (i) al- locations (^ c j ; ^ b j ) and actions ^ d i for economy j 2 J, (ii) allocations for the investor (^ x;f^ z j g J j=1 ), and (iii) bond pricesf^ q j g J j=1 such that 1. For each economy j2 J, given the bond pricesf^ q j g J j=1 , (^ c j ; ^ b j ) and ^ d j solve for the economy's problem. 2. Given the bond pricesf^ q j g J j=1 , (^ x;f^ z j g J j=1 ) solves the investor's problem. 3. For all j2J, ^ q j clears the bond markets, i.e. ^ b j = ^ z j . 2.5 Analysis of Equilibrium This section analyzes the equilibrium of the model. First, the qualitative analysis of equilibrium is provided. Following that, the quantitative analysis is presented. 2.5.1 Parameter Values For the quantitative analysis of the equilibrium, the model is assumed to consist of two emerging economies, i.e. J = 2. The parameter values are chosen such that the business cycle frequency moments simulated are consistent with that of the emerging economies. For the two emerging economies, the representative consumer is assumed to have constant relative risk averse preferences u(c) = c (1) 1 24 Table 2.4: Parameter Values Preference Parameters 2 Constant relative risk aversion rate of emerging economies 0.92 Time discount rate of representative investor 0.89 Time discount rate of emerging economies Endowment Parameters 0.65 Autocorrelation coecient of t 0.034 Standard deviation of t y 1 Mean of endowment m 50 Deterministic income of investor Other Parameters e 5% Annual coupon rate 2% Direct income loss after default with the relative risk aversion rate . The relative risk aversion rate is set to 2. [45] estimates the intertemporal elasticity of substitution for emerging economies within the range of [0:1; 0:8]. The chosen constant relative risk aversion rate is consistent with this range. The representative investor, on the other hand, is assumed to have logarithmic pref- erence u(c) =ln(c) This is a special case of DARA preferences with relative risk aversion rate of 1. With logarithmic utility, the investor will follow a short-term strategy that does not allow its wealth to decline to zero. 25 The representative investor is assumed to discount time at a rate of 0:92. During the 1990s the emerging economies grew at an average rate of 3:3%, with time discount rate corresponding to 0:89 9 . With this discount factor the emerging economies are on average net debtors with an incentive to default. According to [2] the autocorrelation coecients and standard deviations of income of a group of 13 emerging economies 10 stand within the range of [0:5; 0:89] and [1:2%; 4:4%], respectively. Consistent with the data, the AR(1) coecient of the productivity shocks is chosen as 0:65 with a standard deviation of 0:034. Note that with higher persistence the default risk of an emerging economy's sovereign would also be persistent. Moreover, with long-term bonds, the persistence in the default risk would pass on from one period to the other via bond prices. Table 2.5: Real GDP (USD bln), 1995 prices Emerging Economies OECD Economies Ratio 1980 303.4 15,612 51.46 1990 435.5 21,161 48.59 2000 505.5 26,855 53.13 Source: World Bank Development Indicators The income process is approximated by a Markov chain with 3 possible realizations using the quadrature-based technique introduced by [33]. The mean of income is nor- malized to 1. On the other hand, the investor's deterministic income level is set to 50, in units of consumption good. This level can be justied by the large income dierential between industrialized economies and emerging economies. Finally, the annual coupon 9 = (1+g) 1 10 The 13 emerging economies are Argentina, Brazil, Ecuador, Israel, Korea, Malaysia, Mexico, Peru, Philippines, Slovak Republic, South Africa, Thailand, Turkey. 26 rate of the bonds is taken to be 5%. The direct income loss, on the other hand, is set to 2%, in line with the evidence on post-crisis contraction of output. 2.5.2 Properties of Equilibrium 2.5.2.1 Equilibrium Value Functions For a given state of income and fundamentals of other economies, the value of both no-default and default is decreasing over indebtedness and increasing over income. This follows from the property that utility is increasing and concave in consumption. However, the rate of decline in the value of default is always less than the rate of decline in the value of no-default. Thus, there exists a minimum level of indebtedness at which default is optimal (Figure 2.3a). Dene the minimum level of indebtedness as b j (y j j(b ; y )) =argmin n jV d (s)V n (s)j o (2.17) where b =fb k g k2J; k6=j and y =fy k g k2J; k6=j . Following from the property that the value functions are an increasing function of income, b j (y j j(b ; y )) is also an increasing function of income. The intuition is that at high income levels, the net repayment becomes less costly which enables the economy to become more tolerant to indebtedness. 2.5.2.2 Equilibrium Default Policy Each economy's optimal default policy can be characterized by equilibrium default sets and default risk. 27 Denition 2.5.1 Given (b ;y ), the default set is the set of y j for which default is optimal when the economy's debt level isjb j j D j (b j j(b ;y )) = y j 2Y j :d j (s) = 0 (2.18) Since the set of income Y j is compact, there exists a level of indebtedness high enough, such that economy j would prefer to default at all states of income. On the other hand, there also exists a level of indebtedness low enough, such that economy j will not default no matter what the state of income is. Denition 2.5.2 Given (b ;y ), let b j denote the upper bound of bonds j for which the default set is equal to the entire set of income and let b j denote the lower bound of bonds j for which the default set is empty. b j =inffb j 2B j :D j (b j j(b ;y )) =;g b j =supfb j 2B j :D j (b j j(b ;y )) =Y j g Having dened the equilibrium default sets, the equilibrium probability of default, i.e. risk of default, of economy j can be characterized as } j (b j j(b ; y )) = X y j 0 2D j (b j j(b ;y )) f(y j 0 jy j )dy j 0 (2.19) The probability of default monotonically increases over the level of indebtedness. At b j , the probability of default is zero and at b j , the probability of default is one. Finally, for any b j <b j <b j the probability of default takes on a value between zero and one. 28 Property 2.5.1 Given (b ;y ), for all b j 1 b j 2 , if for some level of income y j 2 Y j , default is optimal for a debt level of b j 2 then it is also optimal to default at a debt level of b j 1 , i.e. D j (b j 2 j(b ;y ))D j (b j 1 j(b ;y )). In other words, the default sets shrink as the debt level decreases. Proof 2.5.1 See Appendix A.1. The result follows from the properties that given the level of income, both the value of default and value of no-default is decreasing in indebtedness and that within the default region value of no-default declines faster and is always less than the value of default. Thus, at a given level of income, for any level of indebtedness greater than b j (y j j(b ; y )), the distance between the value of default and value of no-default increases, leaving default less and less costly (Figure 2.3). Property 2.5.2 Given (b ;y ), for all y j 1 < y j 2 , if for some level of bond b j 2 B j , default is optimal for income level y j 2 then it is also optimal to default at income level y j 1 . Proof 2.5.2 See Appendix A.1. The intuition is that at low income, for a highly indebted economy rolling over debt would become more costly as the availability of the debt contracts to increase consumption rel- ative to income would be limited. Therefore, at times of recession and high indebtedness default is preferred. Figure 2.3b displays the aforementioned properties of value functions and equilibrium default policy of economies. The following analysis of equilibrium debt policy and bond prices is induced from the features of the value functions and property 2.5.1. 29 2.5.2.3 Equilibrium Debt Policy The economies prefer to rollover or even increase their indebtedness in order to increase their consumption relative to income. However, as the level of indebtedness increases the economies incur higher cost of borrowing and are restricted to whatever debt they already carry. Property 2.5.3 Given (b ;y ), for any state of incomey j ,jb 0 (s)j is an increasing func- tion ofjb j j. The model delivers countercyclical debt policy, i.e. the economies prefer to borrow more at times of recession compared to those at times of boom (Figure 2.4a). This relation is spelled out when the indebtedness of the economies are low. This is attributed to the fact that for economies with lower indebtedness the number of debt contracts are more and cheaper. Property 2.5.4 Given (b ;y ), for all y j 1 < y j 2 and for some level of bond b j 2 B j , jb 0 (s 1 )jjb 0 (s 2 )j, wheres 1 = (y 1 ;:::;y j 1 ;::::;y J ;b 1 ;:::;b j 1 ;:::;b J ) ands 2 = (y 1 ;:::;y j 2 ;::::;y J ; b 1 ;:::;b j 2 ;:::;b J ). 2.5.2.4 Equilibrium Bond Prices The economy's default policy and the price of its bonds are closely related since the investor incorporates the risk of default into bond prices. Thus, for contracts that propose larger amounts of bond issues, the economy is required to pay a higher interest rate. Moreover, when the economy is in a boom the interest rate charged for any level of borrowing is less, relative to those that are charged during recession (Figure 2.4b). This 30 is attributed to the aforementioned properties of default risk increasing with indebtedness and decreasing with income. Property 2.5.5 Given (b ;y ), for any state of income y j , the price of bond j, q j (s) where s = (y j ;b j ;y ;b ), is an increasing function of bond level b j . Property 2.5.6 Given (b ;y ), for any level of bond j, b j , the price of bond j, q j (s) is an increasing function of the state of income y j . −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 −0.5 −0.475 −0.45 −0.425 −0.4 −0.375 −0.35 −0.325 −0.3 −0.275 −0.25 −0.225 −0.2 Bond Holdings Value w/ Default Value w/ No−Default Optimal Value −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 Bond Holdings Optimal Value @ High Income Optimal Value @ Low Income (a) Value of Default and No-Default 0.8 0.85 0.9 0.95 1 1.05 1.1 −0.9 −0.85 −0.8 −0.75 −0.7 −0.65 −0.6 −0.55 −0.5 −0.45 −0.4 Income Bond Holdings D(−0.5 | (b 2 ,y 2 )) = [0.0,1.06] D(−0.45| (b 2 ,y 2 )) = [0.0,1.00] D(−0.39| (b 2 ,y 2 )) = [0.0,0.91] (b) Equilibrium Default Sets Figure 2.3: Value Functions and Equilibrium Default Policy 31 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Current Indebtedness Future Indebtedness Debt Policy @ High Income Debt Policy @ Low Income (a) Equilibrium Debt Policy −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Bond Holdings Bond Price @ Low Income Bond Price @ High Income (b) Equilibrium Bond Prices Figure 2.4: Equilibrium Debt Policy and Bond Prices 32 2.5.3 Contagion Contagion is an equilibrium outcome when a deterioration in one of the emerging economies' fundamentals propagate default in another economy even when the economy's own fundamentals do not call for it. As was mentioned earlier, an increase in the default risk of one emerging economy would negatively impact the wealth of the representative investor which would in turn increase the debt rollover cost of the other economy to such an extent that default for that economy may become desirable. Section 2.5.3.1 will depict the relation between emerging economies' fundamentals and the representative investor's wealth as well as the changes in the equilibrium policies of an emerging economy with respect to the changes in the fundamentals of other economies. 2.5.3.1 Properties of Equilibrium Denition 2.5.3 Let the representative investor's wealth be !(s), such that !(s) = J X j=1 q j (s) +e (1d j (s)) z j where s is the vector of the fundamentals of the emerging economies which the represen- tative investor lends. Figure 2.5(a) presents the representative investor's wealth in relation to its bond holdings. Within the no-default region, the representative investor's wealth monotonically increases with the bond holdings. However, within the region where default risk is positive the investor's wealth decreases with its bond holdings. The investor's wealth reaches its lowest level when default happens with probability 1. Figure 2.5(b), on the other 33 hand, displays the relation between the representative investor's wealth and the income level of the emerging economies. Accordingly, during recessions, as the default risk of the emerging economies increases the investor's wealth level declines as the bond prices decline. However, during booms, this relation is reversed. The above relation follows from the countercyclical debt-default policy of the emerging economies. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 Bond Holdings, b 2 Bond Holdings, b 1 0.9 0.95 1 1.05 1.1 1.15 0.9 0.95 1 1.05 1.1 0.04 0.06 0.08 0.1 0.12 0.14 Income, y 2 Income, y 1 (a) Wealth versus Outstanding Debt of EE (b) Wealth versus Income of EE Figure 2.5: The Representative Investor's Wealth Figure 2.6 shows the relation between the emerging economies' value functions and the representative investor's wealth. As indebtedness decreases wealth increases. As wealth increases the dierence between the value of no-default decreases while value of default is almost constant. This together with Property 2.5.1 imply the following property of the equilibrium default policy with respective to contagion. Property 2.5.7 Given b j 2 B j , let (b 1 ;y 1 ) and (b 2 ;y 2 ) be the fundamentals of other economies such that b 1 b 2 and y 1 y 2 . The default set of an emerging econ- omy increases as the fundamentals of other economies deteriorate, i.e. D(b j j(b 1 ;y 1 )) D(b j j(b 2 ;y 2 )). 34 −0.9 −0.85 −0.8 −0.75 −0.7 −0.65 −0.6 −0.55 −0.5 −0.45 −0.4 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Wealth −0.9 −0.85 −0.8 −0.75 −0.7 −0.65 −0.6 −0.55 −0.5 −0.45 −0.4 −0.47 −0.465 −0.46 −0.455 −0.45 −0.445 −0.44 −0.435 −0.43 Bond Holdings Value Value of No−default Value of Default Figure 2.6: Wealth versus Value of Default and No-default This result also can be applied to the equilibrium default risk of economies in the following way. Property 2.5.8 Given b j 2 B j , let (b 1 ;y 1 ) and (b 2 ;y 2 ) be the fundamentals of other economies such that b 1 b 2 and y 1 y 2 . The higher the risk of contagion, the higher the default risk of an emerging economy, i.e. }(b j j(b 1 ;y 1 ))}(b j j(b 2 ;y 2 )). 35 Following property 2.5.8, it can be concluded that bond prices of an economy decrease with the risk of contagion, which is attributed to a deterioration in other economies' fundamentals. Property 2.5.9 Given (b j ;y j )2B j Y j , let (b 1 ;y 1 ) and (b 2 ;y 2 ) be the fundamentals of other economies such that b 1 b 2 and y 1 y 2 . As the risk of contagion increases, the bond prices of economy j decreases, i.e. q j (b j ;y j j(b 1 ;y 1 ))q j (b j ;y j j(b 2 ;y 2 )). 2.5.4 Quantitative Analysis of Equilibrium This section presents the quantitative analysis of equilibrium. Section 2.5.4.1 presents the simulation result of the model. Section 2.5.4.2 shows the impulse response simulation to explore the channel through which contagion occurs. Finally, section 2.5.4.3 presents an experiment which was used to dierentiate the eects of contagion and default on bond prices. 2.5.4.1 Simulation Results of The Model The results below are the average of 1000 simulations. In each run, 1000 periods are simulated of which the last 100 observations are collected. The time series is annual. For statistical analysis the relevant variables are HP ltered with a smoothing parameter of 100. Emerging market bonds are rewarding to investors for its excess return. For instance, during the 1990s, the annual average emerging market bond spread was 8:3% 11 . However, according to the data these spreads are also known for its volatile nature. As a measure 11 This value is reported in [31]. 36 Table 2.6: Model Results Sharpe Ratio (mean, annual) 0.20 Spread Correlation 0.49 Debt (mean, % of income) 36.6% Default Probability 10.0% of the excess return per unit of risk, during the 1990s, the Sharpe ratio of emerging bond market was on average 0.59. The model can explain 34% of the actual value by delivering a value of 0.20. During the period of 1994-2001, the correlation between emerging economies' bond spreads varies in the range of [0:37; 0:83]. The correlation between the emerging economies' spreads generated by the model is 0:49. This value explains 60% of the average corre- lation across the emerging economies during the 1990s. In this paper, the correlation between bond prices arise since the investor discounts future payos of both emerging economy bonds via the same stochastic discount factor. The stochastic discount factor is a function of the representative investor's consumption growth which is aected by any credit event. The correlation decreases if the investor is relatively less risk averse, thus less sensitive to changes in his or her value of emerging economy bonds portfolio. According to simulations, the emerging economy's mean debt-to-income ratio is 36:6%. Emerging economies are known to hold large external debt (Table 2.7). During 1990s, emerging economies have changed the composition of their debt, holding more in the form of bonds. The high level of mean debt-to-income ratio is mainly because in this model the emerging economies are allowed to continue to have access to the international 37 nancial markets conditional on some outstanding debt recovery where the recovery rate is determined by the emerging economy 12 . In this model, the assumption of one-period nancial autarky also generates frequent default. This is because default becomes less costly. In this respect, the average default probability in this model is as high as 10%. For the period 1979-1999, [44] has calculated the unconditional default probability of emerging economies as 13:3%. The model results show that the default probability of an emerging economy decreases when the income penalty on emerging economies is higher. 2.5.4.2 Contagion: Impulse-Response Simulations In this section, the contagion eect is studied numerically by simulating emerging economy policy responses to an exogenous income change in another fundamentally in- dependent emerging economy. For the simulation, the equilibrium policy functions for both emerging economies are interpolated across income levels. After interpolation a time series of 11 periods is collected during which one emerging economy's income receives a one-time, one standard deviation, negative income shock and returns to its original level. Initially, the two emerging economies are in their stationary states where both economies receive their mean income. At the beginning of period 1, one of the two economies, hence- forth country 1, receives a negative income shock that results in an initial 3:4 percent drop in its income. After the shock, the income of country 1 recovers, returning to its 12 [48] is the rst to introduce debt recovery in an Eaton-Gersovitz type sovereign default model. In contrast to the model in this paper, nancial autarky lasts for more than one period during which the emerging economies are required to recover part of their outstanding debt. The recovery rate is determined during debt renegotiations that are held between the defaulter and investors. [48] shows that if the bargaining power of the defaulter in debt renegotiations increases, the equilibrium mean debt-to-income would also increase. 38 mean income. Figure 2.7 presents the changes in the emerging economies' income, con- sumption, debt-to-income ratio and bond prices, and investor's consumption and value of emerging market portfolio. The impulse-response simulations show that the adverse shock in country 1 transmits to country 2 through a change in bond prices. 0 2 4 6 8 10 −4 −3 −2 −1 0 0 2 4 6 8 10 −2 0 2 4 Investor’s Wealth 0 2 4 6 8 10 0 5 10 Country 1: Debt−to−Income 0 2 4 6 8 10 0 5 10 Country 2: Debt−to−Income 0 2 4 6 8 10 −4 −2 0 Country 1: Bond Price 0 2 4 6 8 10 −4 −2 0 Country 2: Bond Price 0 2 4 6 8 10 −4 −2 0 Country 1: Consumption 0 2 4 6 8 10 −4 −2 0 Country 2: Consumption 0 2 4 6 8 10 0 5 10 Investor’s Consumption 0 2 4 6 8 10 −1 −0.5 0 0.5 1 Country 1 & 2: Income Figure 2.7: Contagion: Impulse-Response Simulation In period 1, as a result of the adverse income shock, country 1 defaults. This causes an abrupt decline in the representative investor's wealth. As the representative investor's wealth drops, his or her risk aversion increases. Higher risk aversion induces the repre- sentative investor to reduce his or her demand for both risky assets. In equilibrium, the decline in demand for country 1 and country 2 bonds translates into a decline in both countries' bond prices. Note that the decline in country 1's bond price is higher than the decline in country 2. This is relevant since country 1's default translates into higher risk-premia. Now, at a higher cost of borrowing, both countries have to pay more and 39 borrow more to keep their consumption-to-income ratio unchanged. Notice that, despite its default, as of period 2, country 1 can still access the international nancial markets. However, the cost of consumption smoothing for country 1 is higher than country 2. As the one-time negative income shock fades, both countries' bond prices also increase with the declining default risk of the countries accompanied with the decline in their indebt- edness. After period 1, with lower cost of borrowing, country 1 recovers its consumption. 2.5.4.3 Contagion versus Default Eects on Bond Prices In this section, contagion and default eect is decomposed with the use of the equi- librium results of two dierent models. These models are one where both economies are allowed to default and one where both economies are deterred from default. Default is deterred by increasing the default penalty on output. Using the same income series, these two models are simulated for 100 periods. Thus, for each economy there are two sets of bond prices, one with no default risk and one with default risk. From the simulated time series, the periods where only one of the two economies defaulted is sampled to capture the contagion risk. After the selection is made, the bond prices of each economy are compared. For the no-defaulting economy, the dierence between the bond prices in the models with and without default would yield the contagion eect. On the other hand, for the defaulting economy, the dierence between the bond prices in the models with and without default risk would yield the default eect. The dierences are then averaged. This experiment is conducted 1000 times to leave out any outlier eect. Accordingly, the above experiment shows that on average, due to default, prices can decline as much as 40 96:3% for the country that defaults, while contagion would cause a reduction in bond prices of as much as 20:5% for the country that does not default. 2.6 Conclusion Previous studies on contagion have suggested the existence of investors common to all economies as the primary channel of contagious crises of the 1990s. The conventional view is that common investors cause contagion when they fall into liquidity, incentive or coordination problems, or have imperfect information. This paper shows that conta- gion can also be explained via a wealth eect through a general equilibrium incomplete markets model featuring endogenous default and contagion. The model consists of two fundamentally unrelated emerging economies and a continuum of homogenous investors. Emerging economies are modeled as open economies that are non-price takers. Therefore, credit events in emerging bond markets have a non-negligible impact on the world interest rate. Investors are risk averse and follow a short-term investment strategy that avoids declines in their wealth, which is comprised of their portfolio investments in mature and emerging markets. The investors receive a deterministic income from their investments in the mature markets, whereas the income received from their investments in the emerging markets is stochastic because of emerging economies' default risk. In the paper, contagion is triggered by the aforementioned default risk. When an emerging economy defaults or when its default risk increases, investors incur a wealth loss. As a result of this, they become absolutely more risk averse and demand fewer risky bonds, which, in equilibrium, translates into a simultaneous decline in bond demand and 41 prices. A quantitative analysis of the equilibrium shows that this type of investor behavior can explain the high correlation between spreads across countries and the close relation between the emerging market bond spreads and capital ows to emerging economies observed in the data. According to the simulation results, the correlation between bond spreads across countries is on average 0.49, which is 60% of the correlation observed in the data during the 1990s. Also, the impulse response analysis reveals that contagion risk can cause a 20:5% decline in bond prices of emerging economies whose fundamentals do not indicate any default risk. Another dimension along which the model more closely matches the data than previous studies is the mean debt-to-income ratio. The results provide a mean debt-to-income ratio of 36:6% compared to the average ratio of approximately 55% observed in the data. 42 Table 2.7: Total External Debt (% of GDP) Countries 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Argentina 46.05 35.57 30.44 27.69 29.61 38.99 41.77 44.80 48.55 52.80 53.30 Brazil 26.68 30.39 33.68 33.69 28.38 23.16 23.77 25.02 31.33 47.11 40.97 Bulgaria 119.41 116.03 114.47 102.53 81.86 109.01 110.77 91.63 86.29 91.28 Colombia 45.10 43.65 36.64 35.12 27.34 27.55 30.39 30.63 34.20 40.61 41.66 Ecuador 132.38 121.78 111.02 99.53 85.36 72.57 71.56 68.16 70.78 105.73 94.40 Indonesia 63.97 71.64 72.19 58.66 62.63 63.40 58.26 65.01 167.92 116.90 103.70 Malaysia 36.36 36.60 35.74 41.06 42.79 40.55 41.25 49.81 62.11 56.98 50.70 Mexico 41.10 37.29 31.72 33.31 33.97 60.48 48.98 37.98 38.96 35.55 26.53 Nigeria 130.69 134.87 97.50 161.71 155.28 131.69 94.97 83.70 103.33 87.46 83.12 Pakistan 49.510 50.22 50.70 47.32 52.63 49.48 47.26 48.55 52.35 54.28 45.91 Peru 78.65 64.14 58.25 70.26 61.29 59.47 53.31 51.31 55.18 58.41 55.60 Philippines 69.35 71.17 61.64 65.33 61.24 51.71 51.04 59.11 78.11 72.36 76.90 Poland 88.75 72.59 58.65 53.42 44.34 33.04 28.48 27.35 34.45 40.34 39.88 Russia 17.16 26.00 30.97 30.96 32.72 32.20 68.62 92.86 63.25 Thailand 33.33 38.95 38.34 42.72 46.05 60.57 63.51 74.64 97.15 81.31 65.98 Turkey 32.46 33.51 35.26 37.94 50.80 43.06 43.48 43.97 47.48 55.00 58.40 Venezuela 70.34 65.05 64.57 64.42 65.16 47.10 50.04 41.44 40.45 36.99 31.76 Source: World Bank Global Financial Development 43 Chapter 3 In ation Targeting in Emerging Economies: Interest Rate Rules Matter 3.1 Introduction During the 1990s, xed exchange rate regime was proved as an unsustainable monetary policy. After the 1990s, emerging economies started to adopt exible exchange rate regimes with a strong commitment to in ation, by means of interest rate as a policy instrument. As of 2006, emerging economies which adopt the aforementioned monetary policy rule are Brazil, Chile, Mexico, Philippines, South Africa and Turkey. Although there is a growing literature which suggest in ationg targeting for emerging economies, the extend to what type of interest rate rule should be adopted is still being questioned 1 . This paper examines the peformance of four alternative interest rate rule for in ation targeting in an emerging economy. The alternative rules are four types of interest rate rules. The rst is a simple interest rate rule where the domestic interest rate is governed 1 Theoretical studies that examine in ation targeting with simple interest rate rule as an optimal policy for sudden stops are [8], [18]. [42] and [23] discuss the optimality of in ation targeting for emerging economies and develop prescriptions for in ation targeting design. [43] suggest that in ation targeting with a policy rule that defends the exchange rate which also takes private sector's in ation expectations into account could be optimal for emerging economies. 44 by the deviations of current in ation from its respective target value. The second rule is a smoothing interest rate rule where the domestic interest rate adjusts to the deviations of the aforementioned variable but is also restricted within in a band around the previous period's interest rate. The third rule is a forward-looking simple interest rate rule where the domestic interest rate is governed by the deviations of future expected in ation from its respective target value. Finally, the fourth rule is a forward-looking smoothing inter- est rate rule. The model introduced in the paper is a modied version [28] which is a small open economy version of [5] built on the so-called nancial accelerator framework. The nancial accelerator framework is well-known for its competency in explaining the balance sheet problems that arise during nancial crises, mainly in the form of currency mismatches and non-performing loans [[38] and [19]]. This framework has been the ba- sis of papers which study xed versus exible exchange rate policies [[14], [28], [18]] or exchange rate defense via interest rates during nancial crises [[1], [15], [7]]. The quantitative analysis of the model. The rst two analysis are the comparison of alternative in ation targets, CPI versus DPI in ation and of alternative interest rate rules in reducing volatility in the economy. The last analysis is investigation of the response of alternative interest rate rules to a nancial distress, i.e. an unexpected increase in the country's risk premium. According to the results, rst, the model suggests that in targeting in ation the monetary authority should focus on the dynamics of consumer price index rather than domestic price index. This is mainly because when consumer price index is the in ation target the exchange rate becomes a determinant in policy response and this allows the monetary authority to reduce the distortion on the return to capital that arises due to nancial market imperfections and high liability dollarization 45 in the economy. Second, the model suggests that a monetary authority of an emerging economy should adopt forward-looking smoothing interest rate as a policy rule which achieves the least volatility in the economy. Finally, the last analysis suggest that the monetary authority should adopt a regime switching policy in case of a nancial distress, where at the start of the distress the authority adjust the domestic interest rate according to the forward-looking smoothing interest rate rule and, once the economy returns to its pre-shock output level, the authority switches to using the simple interest rate rule. This follows from the simulation results presented in section 3.4. Accordingly, during a nancial distress the contraction in real activity is less under the forward-looking smoothing rule whereas once the recovery starts the growth in real activity is more rapid under simple rule. In the model, a distress is characterized as an unanticipated increase in the foreign interest rate. Under both rules, the unanticipated increase in the foreign interest rate requires an immediate depreciation of the domestic currency and an upward adjustment of domestic interest rate against in ationary pressures. As opposed to the simple rule, under the forward-looking smoothing rule, the upward adjustment in the domestic interest rate is limited. Thus, under the forward-looking smoothing rule, while the domestic interest rate increases less, the domestic currency depreciates more. This has three important implications. First, since under the forward-looking smoothing rule the depreciation of the domestic currency is larger, the country becomes more competitive in the world market. This stimulates the foreign demand for domestic goods, i.e. exports of the country. The increased demand for domestic goods stimulates production in the wholesale sector. Second, the larger depreciation of the domestic currency under the smoothing rule would lead to less demand for foreign goods due to the relatively higher price of the foreign 46 good in domestic currency units. Finally, since under the forward-looking smoothing rule the increase in the domestic interest rate is less than the simple rule, the decline in the asset prices and the rental rate on capital will also be less. This eases the pressure on the rms' nancing and encourages investment thus production. However, after the distress the relation reverses. Under the forward-looking smoothing rule the growth in the real output, consumption, investment is less than that under the simple rule after the sudden stop. This is mainly because, unlike the simple rule, under forward-looking smoothing rule once the economy enters the recovery period the necessary downward adjustment in the interest rate and the corresponding correction in the exchange rate is not as rapid. In section 3.2 the problem is explained and the model is characterized. Section 3.3 introduces the parameter values used for the quantitative analysis of the model. In section 3.4, the results are presented. Finally, in section 3.5 we conclude. 3.2 The Model This is a variant model of [28] which is a small open economy version of the nancial accelerator model introduced in [5] excluding the inclusion of money and price rigidities. The model consists of three types of producers: wholesale, capital and retail sectors, and three types of agents: households who own the retail rms, entrepreneurs who manage the wholesale rms, and capital producers. In the model, there is also a monetary authority which determines the domestic interest rate via a policy rule, a government which follows a balanced budget policy. 47 Brie y, the circular ow in the economy is as follows: the capital producers utilize domestic and foreign nal goods in the production of the capital good; the wholesale producers employ the capital good as an input; the retail rms utilize wholesale goods to produce dierentiated goods that are aggregated into the nal good; the households receive labor income, prots and asset returns from which they can consume a composite good of domestic and foreign nal goods. 3.2.1 Households The household's consumption good,C t , in this economy is a composite of domestic and foreign nal goods,C d t andC f t , respectively. Assuming that the household's intratemporal elasticity of substitution between domestic and foreign goods, , is constant over time, the consumption composite is obtained by C t = 8 > > > > < > > > > : h ( ) 1 (C d t ) 1 + (1 ) 1 (C f t ) 1 i 1 if 0 (C d t ) (C f t ) (1 ) if = 1 (3.1) where 2 (0; 1). Here, determines the relative weights that domestic and foreign nal goods receive in the consumption composite. Given the preferences of the household over domestic and foreign nal goods and the prices, the cost minimization implies the following demand functions C d t = P d t P t C t (3.2) C f t = (1 ) P f t P t ! C t (3.3) 48 and the consumer price index P t P t = 8 > > > > < > > > > : h (P d t ) 1 + (1 ) (P f t ) 1 i 1 1 if 0 (P d t ) (P f t ) (1 ) if = 1 (3.4) whereP d t andP f t are the price of a domestic and foreign nal goods in domestic currency units. On the other hand, the price of the foreign good in units of foreign currency, P f t , can be written as P f t = P W f t S t (3.5) where P W f t is the wholesale price of the foreign good in domestic currency units, and S t is the nominal exchange rate. The above equality implies that at the wholesale level, before pricing in the retail sector, the law of one price holds. Given the characterization of the consumption composite above, the preferences of the household over the composite good and the leisure is represented by E 0 1 X t=0 t u(C t ;L t ) (3.6) where2 (0; 1) is the subjective time discount factor. The period utility function,u(:;:), depends on both consumption, C t , and labor supply, H t , and has the following form u(C t ;H t ) = ln (C t ) H 1+# t 1 +# 49 where # 0 2 . The household optimally splits its income after tax, T t , between consumption and saving in every period subject to the its budget constraint. We assume that the household cannot access the international nancial markets. Thus, they can only trade assets,A t+1 , denominated in domestic currency with a nominal rate of return ofi d t . In equilibrium, the domestic assets exist in zero net supply so that A t = 0 for all t. The household income consists of the nominal wage collected, W t , dividends paid by the retail rms, r;t , and the returns from domestic asset savings (1 +i d t1 )A t . Finally, the budget constraint of the household can be written as P t C t +A t+1 W t H t + r;t T t + (1 +i d t1 )A t (3.7) The household maximizes the expected discounted lifetime utility (3.6) subject to the budget constraint (3.7). The Euler equation resulting from this maximization is given by 1 = E t " (1 +i d t ) C t+1 C t P t P t+1 # (3.8) The Euler equation (3.8) relates the gross nominal interest rate in the domestic market to the expected in ation rate t+1 =P t+1 =P t . The household's choice between consumption of the domestic and foreign good is given by C d t C f t = (1 ) P d t P f t ! (3.9) 2 1 # is the labor supply elasticity with respect to wage 50 Finally, the following equality determines the household's choice between labor versus leisure. 1 C t W t P t = H # (3.10) 3.2.2 Foreign Demand for Domestic Goods The foreign demand for the domestic goods, C d t , is given by C d t = " P d t P t & Y t # " (C d t1 ) 1" (3.11) where " 2 (0; 1), Y t is the exogenously given level of foreign real output, the term (C d t1 ) 1" represents the inertia in foreign demand for domestic products, and & is the price elasticity of foreign demand for the exports. According to this formulation, the exports depend on the foreign real output, price of good in foreign currency units, and the inertia term. Note that at the steady state the economy is assumed to have a balanced trade. 3.2.3 Wholesale Producers The rms in the wholesale market are owned and operated by risk-neutral entrepreneurs. Given the available technology, entrepreneurs combine capital and labor in the produc- tion of wholesale output. They can nance their investment in new capital by using their own funds and through borrowing from foreign nancial markets. Here, it is implicitly 51 assumed that entrepreneurs do not have enough internal funds to fully nance their in- vestment projects. For this purpose, entrepreneurs are assumed to manage a wholesale rm for a limited time period so that they never accumulate enough resources to fully nance purchases of new capital with their internal funds. At the end of every period, the entrepreneurs face a positive probability of exit from entrepreneurship, i.e. 1, 3 . In order for the population of entrepreneurs to remain stationary, every entrepreneur who exits is replaced with a new entrepreneur whose only endowment is his inelastically supplied labor, H e t . This ensures that a new entrepreneur has some initial funds. Wholesale rms are price takers in the competitive market. Let L t and K t be the labor and capital used by entrepreneurs in the production of wholesale good. Labor is a composite of labor supplied by households and the entrepreneur's own labor and is given by L t = H e t H 1 t (3.12) Also, the portion of capital that is employed in wholesale production is measured by the utilization rate u t . The capital utilization rate is endogenously determined by the rm. Denoting real output as Y W t , the production technology is given as Y W t =! t Z t (u t K t ) L 1 t (3.13) where, Z t is the total factor productivity shock which is the only source of aggregate uncertainty, ! t is the idiosyncratic shock to the individual rm, and is the income 3 The expected horizon for an entrepreneur will be 1 1 . 52 share of capital services. The distribution of Z t is publicly known. ! t is a continuous random variable independently and identically distributed across rms and time with mean equal to unity. Given the capital stock, K t , determined at the end of the previous period, t 1, the labor demand of the wholesale rm is expressed as (1)(1 ) Y W t H t = W t P W t (3.14) (1) Y W t H e t = W e t P W t (3.15) where P W t is the nominal price of the domestic wholesale output. On the other hand, the capital available to a wholesale rm in the current period is determined in the previous period. Hence, an entrepreneur chooses the labor and capital utilization rate before purchasing the capital to be used in the next period. Capital depreciates via the production process and the rate of depreciation is assumed to be a convex function of the utilization rate. Following [4], let the depreciation rate have the following form: (u t+1 ) = a + b 1 + (u t+1 ) 1+ (3.16) witha;b; > 0. According to this function, the depreciation of capital is higher at higher rates of capital utilization. The optimality condition for capital utilization is Y W t u t = 0 (u t )K t P I t P W t (3.17) 53 whereP I t denotes the price of new investment goods, and(u t ) is the capital depreciation rate. According to the above expression, the wholesale rm optimally determines the level of capital utilization taking its marginal cost, i.e. capital depreciation, into account. At the end of period t, the rm has to purchase capital which can be used in the subsequent periodt+1 to produce output at that time. The rm nances the acquisition of capital by its own net worth available at the end of the period, and by external nancing. The external nancing is in the form of nominal bonds issued in the international nancial markets. If we denote the capital stock purchased, net worth of the rm in domestic currency and the foreign currency denominated nominal bond issued at time t as K t+1 , N t+1 , and B t+1 , respectively, then the capital nancing can be written as Q K t K t+1 = N t+1 +S t B t+1 (3.18) where Q K t is the nominal price of capital in domestic currency. The demand for capital depends on the expected marginal return on capital and the expected marginal nancing cost. The gross real return of capital, i.e. (1 +r K t+1 ), is given by the following optimality condition E t h 1 +r k t+1 i = E t 2 6 4 P W t+1 Y W t+1 K t+1 +Q K t+1 (u t+1 )P I t+1 Q K t 3 7 5 (3.19) where Y W t+1 K t+1 is the marginal product of capital. In the above equation (3.19) the price of capital re ects the aggregate adjustment costs born by the capital-producing sector. The adjustment costs apply to net capital. To formulate such a specication, the rms 54 are assumed to pay the depreciation costs associated with capital before it is sold in the market. Once the demand for capital is known, given its net worth, the rm's external nancing need is determined. The interest rate charged to the rm for its external nance is more expensive than the internal nance. This is mainly because the lender charges a premium against the rm's risk of repudiation and collateralizes the rm's debt. Accordingly, the premium increases as the rm's leverage ratio, i.e. real debt-to-net worth, increases 4 . Following this, the rm's marginal cost of fund is dened as the product of the gross premium for external nancing, t (:), and the gross real opportunity cost of funds that would arise in the absence of capital market frictions. E t h 1 +r k t+1 i = S t B t+1 N t+1 E t (1 +r f t ) S t+1 S t (3.20) with 0 (:) > 0; 0 (0) = 0; 0 (1) = 1 (3.21) In the above equation, (1+r f t ) is the real interest rate on foreign assets. It is exogenously given. The interest rate includes the country risk premium and therefore is greater than the risk-free interest rate. (1 +r f t ) = t (1 +r rf ) (3.22) 4 The rm's contracting problem for its external nancing is similar to that presented in the working paper version of [28]. 55 Moreover, the interest rate on foreign assets is related to that of domestic assets through uncovered interest parity condition 0 = E t P t P t+1 (1 +i d t ) (1 +i f t ) S t+1 S t (3.23) Equation (3.20) provides the foundation for the nancial accelerator. Accordingly, the rm would demand capital to the extent that its return is no more than its cost of nancing. Equations (3.19) and (3.20) links the movements in the price of capital to the collateral. Another nancial accelerator is the relation that describes the evolution of net worth. Let V t denote the value of rm's capital net of borrowing costs carried over from the previous period. Then, the total net worth of the rms in the wholesale market is the sum of the remaining entrepreneurs value, V t , and wage income of all entrepreneurs W e t H e t : N t+1 = V t +W e t H e t (3.24) with V t = 1 +r k t Q K t1 K t t1 (:) (1 +r f t1 ) S t S t1 S t1 B t (3.25) According to equations (3.24) and (3.25), the movements in the rm's net worth is related to unanticipated movements in exchange rates, returns and borrowing costs. 56 The entrepreneurs who exit at the end of the period t consumes their net worth: P t C e t = (1)V t (3.26) where C e t is the amount of composite consumption good consumed by the exiting en- trepreneurs. 3.2.4 Capital Producers Capital producers are assumed to repair the depreciated capital and to produce new capital goods. New capital is not used to replace the depreciated part of the old capital. Instead, the old capital is repaired by the capital producers as a separate task. Cap- ital producers operate in a competitive market and thus are price takers. They use a composite investment good as an input. The investment good is obtained through I t = ( i ) 1 i (I d t ) i 1 i + (1 i ) 1 i (I f t ) i 1 i i i 1 (3.27) where I d t and I f t are domestic and foreign inputs for capital production 5 , respectively, i 2 (0; 1) quanties the relative weights of domestic and foreign inputs, and i 0 is the intratemporal elasticity of substitution. 5 The inputs are nal goods. 57 Given (3:27), and the prices of domestic and foreign nal goods, P d t and P f t , the cost minimization implies the following demand functions of capital producers for the domestic and foreign inputs I d t = i P d t P I t i I t (3.28) I f t = (1 i ) P f t P I t ! i I t (3.29) where P I t is the price of the composite investment good. The price index for the invest- ment good, P I t , is given by P I t = h ( i )(P d t ) 1 i + (1 i )(P f t ) 1 i i 1 1 i (3.30) The used capital is repaired by the capital producers. Entrepreneurs pay the cost of repairing capital to the capital producers. Since the capital market is competitive, the price the entrepreneurs pay to the capital producers for each unit of depreciated capital repaired is just the price of the investment composite. In this process, (u t )K t units of investment good is used up. Conversely, there are adjustment costs in the production of new capital goods. After production of the wholesale good at time t, the new capital is produced in a competitive market by capital producers. I t units of the investment composite yields It Kt K t units of new capital. The (:) is the adjustment cost function. This function is assumed to exhibit constant returns to scale. Note that the function is concave and increasing with 58 the following two features: () = and 0 () = 1. Thus, the capital accumulation process is written as K t+1 = (1(u t ))K t + I t K t K t : (3.31) It is assumed that the capital producers make their production plans one period in ad- vance in order to capture the delayed response of investment observed in the data. A capital producer rm maximizes its expected prots by choosing I t and K t . A capital producer plans his investment to satisfy the following optimality condition from his prot maximization 6 E t1 Q K t 0 I t K t P I t P t = 0 (3.32) The rst order condition of a capital producer rm with respect to capital 7 is not essential for the solution of the model. 3.2.5 Retail Firms The retail sector is populated by a continuum of monopolistically competitive rms of a unit measure indexed by j2 (0; 1). The production technology in the retail sector uses the domestic wholesale good as input and dierentiates it. During this process, the retailers are assumed to incur a xed cost, . the xed cost is chosen so that at 6 This formulation allows for investment delays. 7 Et1 h Q K t n I n t K t 0 I n t K t I n t K t o l K t i = 0 where l K t is the lease rate of capital. 59 steady-state the retailers' prot is zero. Let Y d t (j) be the amount of the good produced by retailer j. The domestic nal consumption good, Y d t , can then be dened as Y d t = Z 1 0 Y d t (j) r r1 dj r r1 (3.33) The corresponding price of the retail good is also a CES composite of dierentiated prices, P d t (j), P d t = Z 1 0 P d t (j) 1r dj 1 1r (3.34) Cost minimization implies that the demand for each retail good j is Y d t (j) = P d t (j) P d t r Y d t (3.35) The price stickiness in the nal goods market is a la [9], i.e. with probability % that is the same for each retailer, which sets its price independent of the time elapsed since the last adjustment. So the price of the domestic nal good evolves according to P d t = P d t1 % P d t 1% (3.36) where P d t is the optimal price obtained through maximization of the monopolistically competitive retailer rms' expected discounted prots subject to equation (3.36). P d t = 1 i=0 P W t+i (1%)(%) i (3.37) 60 where = 1 11=% is the retail rms' gross markup rate 8 . Combining equation (3.36) and (3.37), we derive an expression for the gross domestic in ation rate (within the neighborhood of a zero-in ation steady state) P d t P d t1 = P W t P d t E t " P d t+1 P d t # (3.38) where = (1%)(1%) % is decreasing in , the measure of price rigidity. We assume the in ation process for the foreign goods sold in the domestic market similar to that of the domestic goods. The in ation rate for foreign nal goods is expressed as P f t P f t1 = f S t P f t P f t ! f E t " P f t+1 P f t # (3.39) where f = (1% f )(1 f % f ) % f . Due to our law of one price assumption, this specication allows for delay in the exchange-rate pass through mechanism. Using equation (3.38) and (3.39) we can write the CPI in ation as P t P t1 = P d t P d t1 ! P f t P f t1 ! (1 ) (3.40) 3.2.6 Government The government is assumed to nance its expenditures by lump-sum taxes collected from the households. Thus, the scal budget is balanced at all times. G t =T t (3.41) 8 We can substitute 3.34 at t-1 into 3.36 for the rst term on the RHS, because the second term is the same for all retail rms. 61 where the government expenditures are exogenous. 3.2.7 Resource Constraint Given the setup of the economy, the resource constraint of the economy is given by Y d t = C d t +C d t +C W t +I d t +G t (3.42) 3.2.8 Monetary Policy In this economy, the monetary authority is committed to implement in ation targeting by means of an interest rate rule. The types of interest rate rules are as follows. In targeting in ation, the monetary authority uses two dierent price index to focus on, the consumer price index (CPI) and the domestic price index (DPI), respectively. The dierence between a CPI and DPI is that the former is a weighted average of the latter and the price of imported goods. Given that the price of imported goods will be assumed constant, targeting CPI as opposed to DPI implies that the exchange rate has a direct impact on the interest rates [18]. 3.2.8.1 Simple Interest Rate Rules The rst rule is a simple interest rate rule where the monetary authority adjusts the nominal interest rate based on current in ation. The simple interest rate rule is characterized as (1 +i d t ) = (1 +r ss ) t (3.43) 62 when CPI is the focus for in ation targeting and (1 +i d t ) = (1 +r ss ) " p d t p d t1 t # pd (3.44) when DPI is the focus for in ation targeting 9 . 3.2.8.2 Smoothing Interest Rate Rules The second rule is smoothing interest rate rule where the monetary authority adjusts the nominal interest rate based on current in ation, and the previous period's interest rate. Thus, under this rule the interest rate adjusts to changes in in ation at a slower pace. The smoothing interest rate rule is characterized as (1 +i d t ) = (1 +r ss ) (1 +i d t1 ) r h t i 1r (3.45) when CPI is the focus for in ation targeting and (1 +i d t ) = (1 +r ss ) (1 +i d t1 ) r 2 4 " p d t p d t1 t # pd 3 5 1r (3.46) when DPI is the focus for in ation targeting. 3.2.8.3 Forward-Looking Simple Interest Rate Rule The third rule is forward-looking simple interest rate rule where the monetary author- ity adjusts the nominal interest rate based on the expected in ation rate. Note that using 9 p d t represents the price of domestic good in real terms. 63 forward-looking interest rate rule, the monetary authority responds to the expectations of the real sector. The forward-looking simple interest rate rule is characterized as (1 +i d t ) = (1 +r ss )E t h t+1 i (3.47) when CPI is the focus for in ation targeting and (1 +i d t ) = (1 +r ss )E t 2 4 " p d t+1 p d t t+1 # pd 3 5 (3.48) when DPI is the focus for in ation targeting. 3.2.8.4 Forward-Looking Smoothing Interest Rate Rule The fourth rule is forward-looking smoothing interest rate rule where the monetary authority adjusts the nominal interest rate based on the expected in ation rate, and the previous period's interest rate. The forward-looking smoothing interest rate rule is characterized as (1 +i d t ) = (1 +r ss ) (1 +i d t1 ) r E t h t+1 i 1r (3.49) when CPI is the focus for in ation targeting and (1 +i d t ) = (1 +r ss ) (1 +i d t1 ) r E t 2 4 " p d t+1 p d t t+1 # pd 3 5 1r (3.50) when DPI is the focus for in ation targeting. 64 3.3 Model Parameters During the 1996-1997 Asian crisis, Indonesia and Korea were the two countries which had the most severe balance sheet problems in the corporate sector, with rms having large debt-to-equity ratios and large foreign exchange exposure. Considering that our model focuses on the rm dynamics, i.e. balance-sheet eect, the model parameters are chosen to stay consistent with certain features of the Korean economy in the 1990s. The parameter values are summarized in Table 3.1. Preferences: The discount factor, is chosen as 0.984. The parameter # in the utility function is set to 0:8. The choice of# corresponds to an elasticity of labor supply, 1 # of 1.25. The elasticity of substitution between domestic and foreign consumption goods, , set to 1. During 1990-2002 Korea's average consumption-to-GDP ratio, C Y , was 0.5. Given this value the share of domestic consumption good in consumption composite, , is set to 0.5. Export Demand: During 1990-2002 Korea's average exports-to-GDP ratio, X Y , was 0.4. So at steady state the exportsC d is taken as 40% of output. The elasticity of export demand, &, is 1 while the inertia in export demand, !, is 0.75. These values are taken from [28]. Government Expenditure: The steady-state government expenditure-to-output ratio, G=Y is set as 0.2 which also implies that the lump-sum tax revenues at steady state was also 20% of the output. Wholesale Good Production: During 1990-2001 Korea's average investment-to- GDP ratio, I Y , was 0.35. To match these values, the share of domestic inputs in investment 65 Table 3.1: Parameter Values Discount factor 0.984 Intra-temporal elast. of subst. in C 1 i Intra-temporal elast. of subst. in I 0.25 Share of domestic goods in C 0.5 # Elasticity of labor supply 1.25 H Hours worked relative to total hours available 1/3 & Elasticity of export demand 1 1" Weight of inertia in export demand 0.75 Capital share 0.5 i Share of domestic goods in I 0.5 C d Y d Exports to output ratio 0.4 G Y d Government expenditures to output ratio 0.2 Share of entrepreneurial labor 0.01 u Steady-state capital utilization rate 1 ( u) Steady-state quarterly capital depreciation rate 0.025 Elast. of marginal depreciation wrt u 1 Steady-state mark-up value 1.2 i k Elast. of q wrt to i k 2 1 Entrepreneur's death rate 0.0477 b Fraction of realized payos lost in bankruptcy 0.12 % Probability of xing prices 0.75 ! Variance of the productivity variable ! 0.28 z Autoregressive coecient of the productivity variable z 0.95 Autoregressive coecient of the country risk premium 0.95 composite, i , and the share of capital in wholesale production,, are set to 0.5. At steady state, the average labor hours is taken as 1 3 . Capital Utilization and Depreciation: The parameter values for the depreciation function and capital utilization are taken from [4]. The steady state utilization rate is 66 assumed as 1. The quarterly depreciation at the steady state, , is 0.025. Finally, the elasticity of marginal depreciation with respect to the utilization rate, is set to 1. Productivity Shock: The total factor of productivity in the wholesale goods tech- nology, Z t , follows an autocorrelation process with an AR(1) coecient of 0.95. On the other hand, the shocks to technological productivity is assumed to follow a normal distribution with mean 0 and variance 1, i.e. Z t N(0; 1). Entrepreneurs: The entrepreneur's death rate is calculated as 0.0477.The share of entrepreneurial labor in total labor, , is set to 0.01. The Contracting Problem: The distribution for the idiosyncratic shock to project yield is taken as log normally distributed with variance 2 ! equal to 0.28, so ln (!) N( 1 2 2 ! ; 2 ! ). Additionally, the idiosyncratic shocks averaged over wholesale rms,E[!], is equal to 1. The fraction of realized payos to banks lost in bankruptcy, b , is set to 12%. Capital Production: The elasticity of substitution between domestic and foreign investment inputs, i is set to 0.25. This value is commonly used in the literature for emerging economies. The share of domestic investment good in the investment composite, i , is set to 0.5. Retail Sector: The mark-up rates for both the domestic and foreign retail sector, and f , are set to 1.2. The elasticity of the price of capital with respect to investment- capital ratio,i k , is taken as 2. The price inertia in the retail sector,%, is set to 0.75. The same value is assumed for the foreign retail sector, % f . Risk Premium: The steady state external nance premium and leverage ratio are taken as 3.5 percent. These values are then used to calculate the parameter capturing 67 the rate of rm risk responding to its leverage ratio. Accordingly, the parameter equals to 0:05. Monetary Policy: In this paper, the performance of various interest rate rules will be assessed. In this respect, the weight on both in ation targets, CPI or DPI, will take on values of 1.1 and 2.0, and the smoothing factor will take on values 0.45, 0.75 and 0.90, respectively. 3.4 Quantitative Results This section presents both the loss of each policy rule obtained through simulations and their impulse responses to sudden stops. 3.4.0.5 Simulation Results The rst goal is to nd out whether a policy prescription of responding to in ation strongly is benecial or not. To compute the benet of the policy rules, a loss function is used. This function is characterized as the average of the variance of the output gap and the variance of in ation. L = 1 2 var ln Y Y ss + 1 2 var (ln()) (3.51) The simulation results suggest that the monetary authority should adopt a strong response to in ation. Figure 3.1 shows the loss of the economy with respect to the weight on in ation in the aforementioned simple interest rate rule where the focus is on consumer price index. 68 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2 3 4 5 6 7 8 9 10 11 12 x 10 −3 Weight on Inflation Figure 3.1: Loss of Simple Interest Rate Rule, CPI The results also suggest that the loss incurred by the economy would be less if the monetary authority focuses on CPI for in ation targeting than DPI [Table 3.2]. Note that when CPI is the in ation target the exchange rate also becomes a determinant in policy response. This enables the monetary authority to reduce the distortion on the return to capital that may arise due to nancial market imperfections and high liability dollarization in the economy. Table 3.2: Simple Interest Rate Rules Weights var ln Y Y ss var(ln()) Loss = 1:1 0.0021 0.0223 0.0122 = 2:0 0.0054 0.0003 0.0028 pd = 1:1 0.0073 0.0064 0.0068 pd = 2:0 0.0091 0.0009 0.0050 69 In addition to these, Table 3.3 10 summarizes the benets of alternative interest rate rules. Accordingly, forward-looking interest rate rule with rst-order smoothing reduces the volatility in the economy substantially owing to reduction in the distortion on the return to capital due to two important factors. With forward-looking interest rate with rst-order smoothing, the monetary authority does not allow sudden jumps or drops in the interest rate thus the rental rate on capital remains stable. Moreover, due to forward- looking feature of the policy, the private sector's expectations are incorporated into the monetary authority's policy response thus avoiding distortions that might arise due to abrupt changes in expectations of the private sector. Table 3.3: Loss of Interest Rate Rules: CPI Weights var ln Y Y ss var(ln()) Loss Simple Interest Rate Rule (Benchmark Rule) = 2:0 0.0054 0.0003 0.0028 Smoothing Interest Rate Rule, r = 0:45 = 2:0 0.0049 0.0003 0.0026 Smoothing Interest Rate Rule, r = 0:75 = 2:0 0.004 0.0004 0.0022 Forward-Looking Simple Interest Rate Rule = 2:0 0.0057 0.0004 0.0031 Forward-Looking Smoothing Interest Rate Rule, r = 0:45 = 2:0 0.0046 0.0004 0.0025 Forward-Looking Smoothing Interest Rate Rule, r = 0:75 = 2:0 0.0034 0.0006 0.002 10 For loss values of alternative interest rate rules where DPI is the focus refer to Table ??. Note that the loss of alternative interest rate rules also suggest that the loss incurred by the economy when DPI is the focus for in ation targeting is higher. 70 3.4.0.6 Impulse Responses This section presents the responses of alternative policy rules to a nancial distress. Each period represents a quarter. The nancial distress is triggered by a one-time 500 basis point unanticipated increase in the country risk-premium. The simulation results are depicted in Figures 3.2-3.5. An unexpected increase in the country's risk premium, i.e. increase in foreign interest rate, is followed by an immediate contraction in the output, consumption and investment followed by a recovery. The recovery in consumption is slower than the output, i.e. by the time the recovery in output is completed consumption is still below its pre-crisis level. However, there is a dierence across rules with respect to the magnitude of contraction. According to the simulation results, under the forward-looking interest rate rule with a rst-order smoothing factor of 0.75 11 , the real activity contracts less than under the other rules. This is because the channels through which these rules induce the observed patterns is dierent. The dierence is even more pronounced between the simple rule and the forward-looking smoothing interest rate rule (Figure 3.6-3.9). The unanticipated increase in the foreign interest rate requires an immediate deprecia- tion of the domestic currency and an upward adjustment of domestic interest rate against in ationary pressures. As opposed to the simple rule, under smoothing interest rate rules the upward adjustment in the domestic interest rate is bounded with the previous period's level. The increase is even more limited under forward-looking smoothing interest rate rule as the shock is unanticipated and the private sector's expectations are still unchanged. 11 The smoothing factor is chosen as 0.75. With a factor 0.45, the dynamics in the economy are almost similar to that of simple interest rate rule. The results suggests that any smoothing factor above 0.45 would generate a smaller contraction and a faster recovery (Figure 3.11-3.14). 71 Thus, under the forward-looking smoothing rule the increase in the domestic interest rate is lower than under the simple rule and others. In addition to this, the depreciation in the domestic currency is larger under the forward-looking smoothing interest rate rule versus the simple interest rate rule and others. This has three important implications. First, since under the forward-looking smoothing rule the depreciation of the domestic currency is larger, the country becomes more competitive in the world market. This stimulates the foreign demand for domestic goods, i.e. exports of the country. The increased demand for domestic goods stimulates production in the wholesale sector. Second, the larger depre- ciation of the domestic currency under the smoothing rule would lead to less demand for foreign goods due to the relatively higher price of the foreign good in domestic currency units 12 . This qualitatively replicates the Korean current account adjustment experience. Figure 3.10 depicts the external balance adjustments under simple and forward-looking smoothing interest rate rule. Finally, since under the forward-looking smoothing interest rate rule the increase in the domestic interest rate is less than under the simple rule and others, the decline in the asset prices and the rental rate on capital will also be the least. This eases the pressure on the rms' nancing and encourages investment. Thus, during the distress under the forward-looking smoothing rule the real activity contracts less compared to the other rules. Therefore, under forward-looking smoothing interest rate rule the welfare loss incurred by the economy is the least. Once the output reaches its pre-shock level, the pick up in real activity is faster under the simple rule. This is mainly because unlike the smoothing rule, under the simple rule once the economy enters the recovery period the necessary downward adjustment in 12 See equation 3.9 for the motivation behind this. 72 the interest rate and corresponding correction in the exchange rate is more rapid. These results suggest that the monetary authority should adopt a regime switching policy, where at the start of a distress the authority adjust the domestic interest rate according to the smoothing rule and, once the economy starts its recovery, the authority switches to using the simple interest rate rule. 3.5 Conclusion Currently emerging economies are adopting exible exchange rate regimes with a strong commitment to in ation targeting, by means of interest rate as a policy instrument. Although there is a growing literature which suggest in ationg targeting for emerging economies, the extend to what type of interest rate rule should be adopted is still being questioned. Using a modied version of [28], i.e. small open economy nancial accelerator model, this paper studies the performance of alternative interest rate rules under in ation targeting. The paper introduces four types of interest rate rules, namely a simple and a smoothing interest rate rule, a forward-looking simple and smoothing interest rate rule, respectively. The model is log-linearized and is quantitatively analyzed. The rst set of results which consists of the simulated loss of the alternative interest rate rules suggest that in targeting in ation the monetary authority should focus on the dynamics of consumer price index rather than domestic price index. This is mainly because the when consumer price index is the in ation target the exchange rate becomes a determinant in policy response and this enables the monetary authority to reduce the distortion on the return to capital that may arise due to high liability dollarization in the economy. Note 73 that under in ation targeting with a special focus domestic price index the monetary authority completely ignores the changes in exchange rate. This in return amplies the distortionary on return on capital due to nancial market imperfections and high liability dollarization within the real sector. The second set of results suggest that among the four alternative interest rate rules, the forward-looking smoothing interest rate rule achieves the least volatility in the economy. The third set of results which is impulse response simulations of the alternative interest rate rules to a nancial distress suggests that a monetary authority of an emerging economy should adopt a regime switching policy, where at the start of a distress the authority adjust the domestic interest rate according to the forward-looking smoothing interest rate rule and, once the economy returns to its pre-shock output level, the authority switches to using the simple interest rate rule. Accordingly, during a distress the contraction is less under the forward-looking smoothing rule whereas once the recovery starts the growth in real activity is more rapid under simple rule. 74 0 1 2 3 4 5 6 −12 −6 0 6 12 18 Output Simple Smooth φ r =0.75 Forward Simple Forward Smooth φ r =0.75 0 2 4 6 −35 −30 −25 −20 −15 −10 −5 0 Household Consumption 0 2 4 6 −50 0 50 100 150 200 250 Investment Figure 3.2: All Interest Rate Rules, CPI I 75 0 2 4 6 −12 −10 −8 −6 −4 −2 0 Labor Productivity Simple Smooth φ r =0.75 Forward Simple Forward Smooth φ r =0.75 0 2 4 6 −20 −15 −10 −5 0 5 10 15 Capital Utilization 0 2 4 6 0 5 10 15 Export Figure 3.3: All Interest Rate Rules, CPI II 76 0 2 4 6 0 2 4 6 8 10 12 Nominal Interest Rate Simple Smooth φ r =0.75 Forward Simple Forward Smooth φ r =0.75 0 2 4 6 −5 0 5 10 Real Domestic Interest Rate 0 2 4 6 0 2 4 6 8 Inflation Figure 3.4: All Interest Rate Rules, CPI III 77 0 2 4 6 0 5 10 15 20 25 30 Exchange Rate Simple Smooth φ r =0.75 Forward Simple Forward Smooth φ r =0.75 0 2 4 6 0 0.5 1 1.5 2 2.5 3 External Finance Premium 0 5 10 15 20 25 30 0 1 2 3 4 5 6 Real Foreign Interest Rate Figure 3.5: All Interest Rate Rules, CPI IV 78 0 2 4 6 −15 −10 −5 0 5 10 15 20 Output Simple Forward Smooth φ r =0.75 0 2 4 6 −35 −30 −25 −20 −15 −10 −5 0 Household Consumption 0 2 4 6 −50 0 50 100 150 200 250 Investment Figure 3.6: Simple versus Forward-Looking Smoothing Interest Rate Rule, CPI I 79 0 2 4 6 −12 −10 −8 −6 −4 −2 0 Labor Productivity Simple Forward Smooth φ r =0.75 0 2 4 6 −20 −15 −10 −5 0 5 10 15 Capital Utilization 0 2 4 6 0 5 10 15 Export Figure 3.7: Simple versus Forward-Looking Smoothing Interest Rate Rule, CPI II 80 0 2 4 6 0 2 4 6 8 10 Nominal Interest Rate Simple Forward Smooth φ r =0.75 0 2 4 6 −2 0 2 4 6 8 Real Domestic Interest Rate 0 2 4 6 0 1 2 3 4 5 6 7 Inflation Figure 3.8: Simple versus Forward-Looking Smoothing Interest Rate Rule, CPI III 81 0 2 4 6 0 5 10 15 20 25 30 Exchange Rate Simple Forward Smooth φ r =0.75 0 2 4 6 0 0.5 1 1.5 2 2.5 3 External Finance Premium 0 5 10 15 20 25 30 0 1 2 3 4 5 6 Real Foreign Interest Rate Figure 3.9: Simple versus Forward-Looking Smoothing Interest Rate Rule, CPI IV 82 0 5 10 15 20 0 3 6 9 12 15 18 21 24 27 Exchange Rate Simple Forward Smooth φ r =0.75 0 5 10 15 20 0 10 20 30 40 50 60 70 80 Net Exports 0 5 10 15 20 0 5 10 15 Exports 0 5 10 15 20 −80 −60 −40 −20 0 20 Imports Figure 3.10: External Balance Adjustments: Simple Rule versus Forward-Looking Smoothing Rule 83 0 2 4 6 −10 −5 0 5 10 15 Output φ r =0.45 φ r =0.75 φ r =0.90 0 2 4 6 −35 −30 −25 −20 −15 −10 −5 0 Household Consumption 0 2 4 6 −50 0 50 100 150 200 250 Investment Figure 3.11: Forward-Looking Smoothing Interest Rate Rule: Dierent Smoothing Fac- tors, CPI I 84 0 2 4 6 −12 −10 −8 −6 −4 −2 0 Labor Productivity φ r =0.45 φ r =0.75 φ r =0.90 0 2 4 6 −15 −10 −5 0 5 10 15 Capital Utilization 0 2 4 6 0 5 10 15 20 25 Export Figure 3.12: Forward-Looking Smoothing Interest Rate Rule: Dierent Smoothing Fac- tors, CPI II 85 0 2 4 6 0 2 4 6 8 10 Nominal Interest Rate φ r =0.45 φ r =0.75 φ r =0.90 0 2 4 6 −10 −5 0 5 10 Real Domestic Interest Rate 0 2 4 6 0 2 4 6 8 10 12 Inflation Figure 3.13: Forward-Looking Smoothing Interest Rate Rule: Dierent Smoothing Fac- tors, CPI III 86 0 2 4 6 0 10 20 30 40 50 60 Exchange Rate 0 2 4 6 −2 −1 0 1 2 3 External Finance Premium 0 5 10 15 20 25 30 0 1 2 3 4 5 6 Real Foreign Interest Rate φ r =0.45 φ r =0.75 φ r =0.90 Figure 3.14: Forward-Looking Smoothing Interest Rate Rule: Dierent Smoothing Fac- tors, CPI IV 87 Reference List [1] Philippe Aghion, Philippe Bacchetta, and Abhijit Banerjee. 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Working Paper, 2006. 91 Appendix A Numerical Appendix A.1 Proofs of The Equilibrium Features of The Three-Country GEIM Model Property A.1.1 Given (b;y), for all b j 1 b j 2 , if for some level of income y j 2 Y j , default is optimal for a debt level of b j 2 then it is also optimal to default at a debt level of b j 1 , i.e. D j (b j 2 j(b;y))D j (b j 1 j(b;y)). In other words, the default sets shrink as the debt level decreases. Proof A.1.1 Take any y 2 2D j (b j 2 j(b;y)) such that for s = (b 2 ;y 2 ;b;y), V d (s)V n (s). Now, suppose y 2 3 D j (b j 1 j(b;y)) that is for ~ s = (b 1 ;y 2 ;b;y), V d (~ s) < V n (~ s). The above relations and the property that both the value of default and no-default are increasing functions of bond holdings imply V d (s) V n (s) V n (~ s) > V d (~ s). However, within the default region V d (~ s) V n (s) always holds which is a contradiction. Thus, y 2 2 D j (b j 1 j(b;y)) and D j (b j 2 j(b;y))D j (b j 1 j(b;y)). Property A.1.2 Given (b;y), for all y j 1 <y j 2 , if for some level of bond b j 2B j , default is optimal for income level y j 2 then it is also optimal to default at income level y j 1 . Proof A.1.2 Let y j 2 2 Y j and b j 2 B j are such that V d (s) V n (s), where s = (b j ;y j 2 ;b;y). Now, take any y j 1 < y j 2 2 Y j and suppose that V d (~ s) < V n (~ s), for ~ s = (b j 2 ;y 1 ;b;y). The above relations implyV d (s)V n (s)V n (~ s)>V d (~ s). However, given that value of default and no-default are increasing function of income and that default is optimal at y j 2 then it is true that V n (~ s) V d (s) which is a contradiction. Thus, for all y j 1 < y j 2 , if default is optimal for income level y j 2 then it is also optimal to default at income level y j 1 . A.2 Solving The Three-Country GEIM Model In order to solve the above recursive problem we use the backward-solution method, i.e. solving the model from period T to 1. Dene and discretize the state space, i.e. s, as the vector (y 1 ;y 2 ;b 1 ;b 2 ), that represent the endowment levels and the asset positions of the two countries, respectively. As mentioned above each economy has 3 endowment 92 levels. Each economy's bond space, on the other hand, is discretized with 41 grids. The debt limit B is chosen so that the no Ponzi scheme holds. The solution algorithm is as follows. Step 1: For each economy i, calculate period T values of default and no-default, i.e. V i;d T (s) and V i;n T (s) for all possible states s. Given the terminal condition b i T +1 = 0, the value of default and no-default at period T will be V i;n T (s) =u y i T + (q i T +d)b i T (A.1) V i;d T (s) =u y i T (A.2) Find the equilibrium default strategy for each state s, I i T (s) = ( 1 if V i;n T (s)V i;d T (s) 0 otherwise (A.3) and the default set D i T (b i ; (b i ;y i )) = y i 2Y i :I i T (s) = 0 (A.4) Given both countries' default policy and the terminal conditions, calculate the investor's marginal utility for period T , i.e. v 0 T (s) = 0 @ y c X i=1;2 (1 +d)I i T1 (s)b i T 1 A 1 (A.5) Step 2: This step involves several substeps which should be repeated for all periods =T 1;:::; 1. 1. For all s, calculate E v 0 +1 (s)(1 +d)I i +1 (s) if =T 1, i.e. X y 2 +1 X y 1 +1 v 0 +1 (s) (1 +d)I i +1 (s)f(y 1 +1 jy 1 )f(y 2 +1 jy 2 ) (A.6) or calculate E v 0 +1 (s)(q i +1 (s) +dI i +1 (s)) if <T 1, i.e. X y 2 +1 X y 1 +1 v 0 +1 (s) (q i +1 (s) +dI i +1 (s))f(y 1 +1 jy 1 )f(y 2 +1 jy 2 ) (A.7) To ease the notation, we dene the above values as m i +1 . Note that given (y 1 ;y 2 ), m i +1 is a function of (b 1 +1 ;b 2 +1 ;b 1 +2 ;b 2 +2 ) where the asset levels for periods + 1 and + 2 are known since we are solving the problem backwards. 93 2. For all s and given m i +1 , solve for the bond prices q 1 and q 2 using the following non-linear system of equations q 1 = m 1 +1 [(b 1 +1 ;b 2 +1 ;b 1 +2 ;b 2 +2 )jy 1 ;y 2 ] y c (q 1 +dI 1 (s))b 1 (q 2 +dI 2 (s))b 2 +q 1 b 1 +1 +q 2 b 2 +1 q 2 = m 2 +1 [(b 1 +1 ;b 2 +1 ;b 1 +2 ;b 2 +2 )jy 1 ;y 2 ] y c (q 1 +dI 1 (s))b 1 (q 2 +dI 2 (s))b 2 +q 1 b 1 +1 +q 2 b 2 +1 (A.8) Notice that the bond prices should be solved for all combinations of (b 1 +1 ;b 2 +1 ;I 1 ;I 2 ) since in period + 1, countries' debt-default policy for period is yet not known. 3. This step should be solved for each country i, separately. Now, for all s and (b i +1 ;I i ), and given the bond prices, ^ q 1 (b 1 +1 ;b 2 +1 ;I 1 ;I 2 ) and ^ q 2 (b 1 +1 ;b 2 +1 ;I 1 ;I 2 ), solve the following maximization problems for all i V i;n (s;b i +1 ;I i ) = max Bb i +1 0 8 > > < > > : u y i +db i + ^ q i (b i +1 ;b i +1 ; 1;I i ) (b i b i +1 ) ! +EV i;o +1 (s 0 ) 9 > > = > > ; (A.9) V i;d (s;b i +1 ;I i ) = max b i b i +1 0 ( u y i + ^ q i (b i +1 ;b i +1 ; 0;I i ) (b i b i +1 ) +EV i;o +1 (s 0 ) ) (A.10) Find the equilibrium default strategy for each state s ^ I i (s;b i +1 ;I i ) = ( 1 if V i;n (s;b i +1 ;I i )V i;d (s;b i +1 ;I i ) 0 otherwise (A.11) and the default set D i (b i ; (b i ;y i )) = n y i 2Y i : ^ I i (s) = 0 o (A.12) Notice that the country i's debt-default policy can only be characterized as a best response function ^ b i +1 (s) =g(b i +1 ; ^ I i ;I i ). 4. Given the best response debt-default policies of each country, solve for the equilib- rium debt policy as follows, for country i ^ b i; +1 (s) =g(b i; +1 ; ^ I i ;I i ) (A.13) where equilibrium default policy is ^ I i (s) =I i (s; ^ b i; +1 ; ^ I i ) (A.14) 94 5. Given the equilibrium debt-default policies, solve for each country i's optimal value for period V i;o (s) = ( V i;n (s; ^ b i; +1 ; ^ I i ) if ^ I i = 1 V i;d (s; ^ b i; +1 ; ^ I i ) if ^ I i = 0 (A.15) 6. For all s and given the equilibrium debt-default policies, solve for the investor's marginal utility at time , i.e. v 0 (s) v 0 (s) = 0 @ y c X i=1;2 (^ q i +d) ^ I i (s)b i + ^ q i ^ b i +1 1 A 1 (A.16) A.3 Solving The SOE Financial Accelerator Model A.3.1 System of Equations Production Function: y t =z t (u t k t ) h e t h (1 ) t (1) (A.17) Labor market equilibrium: h (1+#) t = (1)(1 )p w t y t 1 c t (A.18) Capital stock law of motion 1 : k t+1 = (1(u t ))k t + x t k t k t (A.19) Exports: c d t = p d t s t y t c d (1 ) t1 (A.20) Entrepreneur's net worth: n t+1 = 2 6 4 1 +r k t q t1 k t n t q t1 k t 1 +r f t1 s t s t1 (q t1 k t n t ) (1) y t p w t 3 7 5 (A.21) Feasibility Condition: y t =c d t + c d t + i d t + c e d t (A.22) 1 To avoid notational confusion investments is dened as xt. 95 In ation: t = p w t p d t f s t p f t p f t ! f E t [ t+1 ] (A.23) Country Interest Rate: (1 +r f t ) = t (1 +r rf ) (A.24) Euler Equation: 1 =E t " (1 +r d t ) c t+1 c t # (A.25) Expected Marginal Return on Capital: E t h 1 +r k t+1 i = E t h p w t+1 y t+1 k t+1 +q t+1 p i t+1 (u t+1 ) i q t (A.26) Capital Demand: E t h 1 +r k t+1 i = n t+1 q t k t+1 E t (1 +r f t ) s t+1 s t (A.27) Uncovered Interest Parity: E t (1 +r d t ) (1 +r f t ) s t+1 s t = 0 (A.28) Q-investment Relation: E t q t+1 0 x t+1 k t+1 p i t+1 = 0 (A.29) Domestic Price In ation: p d t p d t1 ! t = p w t p d t E t " p d t+1 p d t t+1 # (A.30) Household Consumption of Domestic Good: c d t = c t p d t (A.31) Domestic Input for Investment Good: x d t = p i t p d t i x t (A.32) 96 Entrepreneur's Consumption for Domestic Good: c e d t = c e t p d t (A.33) Entrepreneur's Total Consumption: c e t = 1 [n t+1 (1) y t p w t ] (A.34) Nominal Domestic Interest Rate: (1 +i d t1 ) = t (1 +r d t1 ) (A.35) Monetary Policy Rules: Simple Interest Rate Rule: (1 +i d t ) = (1 +r ss ) t " p d t p d t1 t # pd Smoothing Interest Rate Rule: (1 +i d t ) = (1 +r ss ) (1 +i d t1 ) r 2 4 t " p d t p d t1 t # pd 3 5 1r Forward-Looking Simple Interest Rate Rule: (1 +i d t ) = (1 +r ss )E t 2 4 t+1 " p d t+1 p d t t+1 # pd 3 5 Forward-Looking Smoothing Interest Rate Rule: (1 +i d t ) = (1 +r ss ) (1 +i d t1 ) r E t 2 4 t+1 " p d t+1 p d t t+1 # pd 3 5 1r A.3.2 Non-Stochastic Steady-State First, the steady-state in ation and price of capital are normalized at 0% and 1, = 1 q = 1 97 Due to the capital adjustment cost function, the latter implies that the price of investment good is 1. p i = 1 From (3.30) and (3.4), p d = 1 p f = 1 From (3.38) and (3.39) p w = 1 p w f = 1 f Assuming that the price of foreign good in foreign currency is 1, the exchange rate at steady-state is also 1= f . From (3.8) and (3.23) R d = 1 R d =R f From the denition of the external nance premium s = R k R f = qk n the R k is found, where and k=n are calibrated. From (3.19) the steady-state capital stock is R k =p w y k (u) Given the capital-net worth ratio k=n the entrepreneur's net worth n is derived. From (3.31) the steady-state investment is i =(u)k Then the steady-state domestic input for investment good is given as i d = i i Given h = 0:3 and z = 1 the steady-state wholesale output is y w =z(uk) (h (1 ) ) (1) 98 From (3.26) and (3.24), the entrepreneur's consumption and the probability of exit from entrepreneurship are given as c e = 1 [n (1) y w p w ] R k = n + (1) y w p w n The steady-state entrepreneur's consumption of domestic good is c e d = c e As is mentioned in the text, the xed cost for retailers, is chosen to set the steady-state prot is zero. Thus the steady-state output level is y d = (1)y w From the labor market equilibrium, (3.10) and (3.12), the steady-state consumption is found h (1+#) = (1)(1 )p w y 1 c The steady-state consumption of domestic good is given as c d = c Finally, given the exports-to-output, c d =y d , and the government expenditure-to-output ratio, g=y d , the feasibility constraint is checked. y d =c d +i d +c e d +c d +g A.3.3 Log-Linearization The solution to the model is characterized as: X t =P X t1 +Qz t (A.36) where X t = h ~ k t+1 ; ~ n t+1 ; ~ h t ; ~ y t ; ~ x t ; ~ x d t ; ~ c t ; ~ c d t ; ~ c e t ; ~ c e d t ; ~ c d t ; ~ p d t ; ~ p w t ; ~ t ; ~ r k t ; ~ q t ; ~ i d t ; ~ r d t ; ~ r f t ; ~ s t i and Z t = h t ;z t ;y t ;p f t i 99 Given that (p d ) (p f ) 1 = 1 and the price of investment good is the composite of p d and p f , ~ p i t = 0 at all times. Therefore, it has been excluded from the log-linearized system. 0 = ~ y t z t ~ k t (1) (1 ) ~ h t (A.37) 0 = ~ y t + ~ p w t (1 +#) ~ h t ~ c t (A.38) 0 = ~ k t+1 x ~ x t (1(u))k t 0 (u)uu t (A.39) 0 = ~ c d t ~ s t ~ y t (1 )~ c d t1 + ~ p d t (A.40) 0 = 2 6 6 6 6 6 6 6 6 6 4 n ~ n t+1 R k qk ~ r k t + R k nR k qk r f t1 + R k nR k qk [q t1 k t ] + R k nR k qk +R k n ~ n t +R k (nqk) [s t s t1 ] (1) y w p w [~ y t + ~ p w t ] 3 7 7 7 7 7 7 7 7 7 5 (A.41) 0 = y d ~ y t c d ~ c d t i d ~ i d t c e d ~ c e d t (A.42) 0 = ~ r f t ~ t (A.43) 0 = ~ i d t ~ r d t ~ t+1 (A.44) 0 = ~ c d t ~ c t +p d t (A.45) 0 = ~ c e d t ~ c e t +p d t (A.46) 0 = ~ x d t ~ x t + i ~ p d t (A.47) 0 = c e ~ c e t 1 [n ~ n t (1) y w p w (~ y t + ~ p w t )] (A.48) 0 = E t h t ~ p w t + f (1 ) s t +p f t t+1 i (A.49) 0 = E t h ~ r d t + (~ c t ~ c t+1 ) i (A.50) 0 = E t 2 6 4 R k q h ~ r k t+1 + ~ q t i p w y w k h ~ p w t+1 + ~ y t+1 ~ k t+1 i q ~ q t+1 3 7 5 (A.51) 0 = E t h ~ r k t+1 ~ r f t h ~ n t+1 ~ q t ~ k t+1 i ~ s t+1 + ~ s t i (A.52) 0 = E t h ~ r d t ~ r f t ~ s t+1 + ~ s t i (A.53) 0 = E t h ~ q t+1 i k (~ x t+1 ~ k t+1 ) i (A.54) 0 = E t h ~ t + (1 + +)~ p d t ~ p d t1 h ~ p d t+1 + ~ t+1 i ~ p w t i (A.55) Monetary Policy Rules: Simple Interest Rate Rule: ~ i d t ( + pd + s )~ t pd [~ p d t ~ p d t1 ] = 0 100 Smoothing Interest Rate Rule: = ~ i d t r i d t1 (1 r ) [( + pd + s )] ~ t + pd [~ p d t ~ p d t1 ] = 0 Forward-Looking Simple Interest Rate Rule: E t h ~ i d t ( + pd + s )~ t+1 pd [~ p d t+1 ~ p d t ] i = 0 Forward-Looking Smoothing Interest Rate Rule: E t h ~ i d t r ~ i d t1 (1 r ) h ( + pd + s )~ t+1 + pd [~ p d t+1 ~ p d t ] ii = 0 Exogenous Processes: t+1 = l t + l t+1 ; l t+1 N(0; 2 l ) (A.56) z t+1 = z z t + z t+1 ; z t+1 N(0; 2 z ) (A.57) y t+1 = y y t + y t+1 ; y t+1 N( y ; 2 y ) (A.58) p f t+1 = pf p f t + pf t+1 ; pf t+1 N(0; 2 pf ) (A.59) 101 Appendix B Data Appendix B.1 Summary of Data Data Frequency Period J.P. Morgan EMBI and EMBI+ Daily 1990-2001 Institutional Investor Ratings Bi-annual 1994-2001 International Financial Statistics Monthly and Annual 1990-2001 IMF World Economic Outlook Annual 1980-2000 World Bank Global Development Finance Annual 1980-2001 World Bank Economic Development Indicators Annual 1980-2001 World Trade Organization Trade Data Monthly and Annual 1994-2001 EMBI+: The J.P. Morgan's Emerging Market Bond Index Plus tracks total re- turns for traded external debt instruments in the emerging markets. The index includes US-dollar-and other foreign currency-denominated Brady bonds, loans, Eurobonds, and local markets instruments. The EMBI+ includes 16 countries that are Brazil, Mexico, Argentina, Venezuela, Poland, Bulgaria, Ecuador, Peru, Panama, Russia, Morocco, Nige- ria and South Korea, Philippines, Colombia, Turkey. The EMBI+ is constructed as a "composite" of its four markets: Brady bonds, Eurobonds, US dollar local markets, and loans. The construction follows the following steps: A daily total return for each single instrument is computed. For each market, an arithmetic, market-capitalization-weighted average of the daily total returns of the constituent instruments is constructed. An arithmetic, market-capitalization-weighted average of the four markets' average daily total returns, calculated above, is constructed. The result is a composite return for the overall EMBI+ market. Instruments in the EMBI+ must initially meet four eligibility criteria: An instrument must have a minimum of US$500 million outstanding. 102 An instrument must meet a BBB+/Baa1 or below rating requirement, designed to dene "emerging markets" in the context of external debt markets. The instrument must have more than a year remaining to maturity. The instrument must be able to settle internationally, such as via Euroclear. Once the eligibility requirements are met, liquidity criteria are applied to the instruments. The bonds that can be included to the index should have an L1 or L2 rating. L1 rating corresponds to bonds with average bid/oer ratio that is lower than 3=8, and bonds that are quoted by at least ve designated brokers. L2 rating corresponds to bonds with average bid/oer ratio that is lower than 3=4, and bonds that are quoted by at least three designated brokers. EMBI: The J.P. Morgan's Emerging Market Bond Index tracks total returns of traded market for U.S. dollar-denominated Brady and other similar sovereign restructured bonds. The EMBI includes 12 countries that are Argentina, Brazil, Bulgaria, Ecuador, Mexico, Nigeria, Panama, Peru, Philippines, Poland, Russia and Venezuela. The EMBI is a subset of the EMBI+. The methodology used in constructing the index is similar to that of EMBI+. IIR: The Institutional Investor Ratings are constructed bi-annually and are reported in March and September. These ratings are based on information provided by economists and sovereign risk analysts at leading global banks and securities rms. IIR grades each country on a scale from 0 to 100, where 100 is given to those countries perceived to have the least chance of defaulting on their sovereign debt obligations. The International Monetary Fund's World Economic Outlook Database: In this database, for the net capital ows the list of countries under each region is given as: Emerging Economies: Albania, Algeria, Angola, Antigua and Barbuda, Argentina, Armenia, Azerbaijan, Bahamas, The, Bahrain, Bangladesh, Barbados, Belarus, Belize, Benin, Bhutan, Bolivia, Botswana, Brazil, Bulgaria, Burkina Faso, Burundi, Cambodia, Cameroon, Cape Verde, Central African Republic, Chad, Chile, China, Colombia, Co- moros, Congo, Democratic Republic of, Congo, Republic of, Costa Rica, Cte d'Ivoire, Croatia, Czech Republic, Djibouti, Dominica, Dominican Republic, Ecuador, Egypt, El Salvador, Equatorial Guinea, Estonia, Ethiopia, Fiji, Gabon, Gambia, The, Geor- gia, Ghana, Grenada, Guatemala, Guinea, Guinea-Bissau, Guyana, Haiti, Honduras, Hungary, India, Indonesia, Iran, Islamic Republic of, Jamaica, Jordan, Kazakhstan, Kenya, Kiribati, Kuwait, Kyrgyz Republic, Lao People's Democratic Republic, Latvia, Lebanon, Lesotho, Libya, Lithuania, Macedonia, Former Yugoslav Republic of, Madagas- car, Malawi, Malaysia, Maldives, Mali, Malta, Mauritania, Mauritius, Mexico, Moldova, Mongolia, Morocco, Mozambique, Myanmar, Namibia, Nepal, Nicaragua, Niger, Nige- ria, Oman, Pakistan, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Poland, Qatar, Romania, Russia, Rwanda, Samoa, So Tom and Prncipe, Saudi Arabia, Senegal, Seychelles, Sierra Leone, Slovak Republic, Solomon Islands, South Africa, Sri Lanka, St. Kitts and Nevis, St. Lucia, St. Vincent and the Grenadines, Sudan, Suriname, Swaziland, Syrian Arab Republic, Tajikistan, Tanzania, Thailand, Togo, Tonga, Trinidad and To- bago, Tunisia, Turkey, Turkmenistan, Uganda, Ukraine, United Arab Emirates, Uruguay, Uzbekistan, Vanuatu, Venezuela, Vietnam, Yemen, Republic of, Zambia, Zimbabwe 103 Asia, crisis countries: Bangladesh, Bhutan, Cambodia, China, Fiji, India, Indone- sia, Kiribati, Korea, Lao People's Democratic Republic, Malaysia, Maldives, Myanmar, Nepal, Pakistan, Papua New Guinea, Philippines, Samoa, Solomon Islands, Sri Lanka, Thailand, Tonga, Vanuatu, Vietnam Middle East including Turkey: Bahrain, Egypt, Iran, Islamic Republic of, Jordan, Israel, Kuwait, Lebanon, Libya, Oman, Qatar, Saudi Arabia, Syrian Arab Republic, Turkey, United Arab Emirates, Yemen Western Hemisphere: Antigua and Barbuda, Argentina, Bahamas, The, Barbados, Belize, Bolivia, Brazil, Chile, Colombia, Costa Rica, Dominica, Dominican Republic, Ecuador, El Salvador, Grenada, Guatemala, Guyana, Haiti, Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, St. Kitts and Nevis, St. Lucia, St. Vincent and the Grenadines, Suriname, Trinidad and Tobago, Uruguay, Venezuela 104
Abstract (if available)
Abstract
This dissertation consists of two essays. The first essay brings a competing explanation for the channel of contagious emerging market crises of the 1990s. It develops a three-country GEIM model to show a debt crisis in one emerging market country transmits to others via common investors through the world interest rate. This constitutes an alternative explanation to the literature suggesting that contagion is due to liquidity, incentives problems or imperfect information or flight to quality. Quantitative analysis of the equilibrium show that the model can explain 60% of the correlation across the emerging market bond spreads since the 1990s. The high correlation across the spreads has often been documented by papers as an important indicator of financial contagion even at times of no-crisis. Additionally, the model can explain 50% of the average debt-to-GDP ratio observed across emerging market economies during the 1990s. One of the goals of any model in sovereign default literature is to generate an equilibrium that sustains a large debt-to-income ratio. The second essay contributes to the literature in proposingalternative interest rate rules for in inflation targeting. It introduces a SOE model built on the financial accelerator framework. The model is solved quantitatively and simulated. First set of results suggest that in targeting in ation the dynamics of consumer rather than domestic price index should be the focus. This is mainly because when consumer price index is the target the exchange rate becomes a determinant in policy response and enables the authority to reduce the distortion on the return to capital that may arise due to liability dollarization.
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Closing the safety gap for airlines in emerging markets using the gap analysis model
Asset Metadata
Creator
Volkan, Engin
(author)
Core Title
Emerging market financial crises, investors and monetary policy
School
College of Letters, Arts and Sciences
Degree
Doctor of Philosophy
Degree Program
Economics
Publication Date
07/22/2008
Defense Date
04/08/2008
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
emerging market financial crises,financial contagion,forward-looking monetary rules,inflation-targeting,interest rate rules,OAI-PMH Harvest,risk-averse investors,sovereign default risk
Language
English
Advisor
Quadrini, Vincenzo (
committee chair
), Dekle, Robert (
committee member
), Zapatero, Fernando (
committee member
)
Creator Email
volkan@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m1379
Unique identifier
UC173051
Identifier
etd-Volkan-20080722 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-194357 (legacy record id),usctheses-m1379 (legacy record id)
Legacy Identifier
etd-Volkan-20080722.pdf
Dmrecord
194357
Document Type
Dissertation
Rights
Volkan, Engin
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
emerging market financial crises
financial contagion
forward-looking monetary rules
inflation-targeting
interest rate rules
risk-averse investors
sovereign default risk